## Holopainen, Ilkka

Compute Distance To:
 Author ID: holopainen.ilkka Published as: Holopainen, Ilkka; Holopainen, I. External Links: MGP
 Documents Indexed: 43 Publications since 1990, including 1 Book Co-Authors: 21 Co-Authors with 33 Joint Publications 418 Co-Co-Authors
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### Co-Authors

 10 single-authored 9 Castéras, Jean-baptiste 7 Rickman, Seppo Uolevi 5 Heinonen, Esko 5 Ripoll, Jaime Bruck 3 Pankka, Pekka 2 Coulhon, Thierry 2 Saloff-Coste, Laurent 2 Shanmugalingam, Nageswari 2 Soardi, Paolo Maurizio 2 Tyson, Jeremy T. 2 Vähäkangas, Aleksi 1 Balogh, Zoltán M. 1 de Lira, Jorge Herbert Soares 1 Heinonen, Juha 1 Koskela, Pekka 1 Lang, Urs 1 Lira, Jorge H. S. 1 Markvorsen, Steen 1 Palmer, Vicente 1 Pigola, Stefano 1 Veronelli, Giona
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### Serials

 5 Proceedings of the American Mathematical Society 4 Mathematische Zeitschrift 4 Revista Matemática Iberoamericana 3 Mathematische Annalen 3 Potential Analysis 2 The Journal of Geometric Analysis 2 Geometric and Functional Analysis. GAFA 2 Annales Academiae Scientiarum Fennicae. Mathematica 1 Israel Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Collectanea Mathematica 1 Duke Mathematical Journal 1 Manuscripta Mathematica 1 Proceedings of the London Mathematical Society. Third Series 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Communications in Analysis and Geometry 1 The Journal of Analysis 1 The Journal of Fourier Analysis and Applications 1 Annales Academiæ Scientiarum Fennicæ. Series A I. Mathematica. Dissertationes 1 Advances in Calculus of Variations 1 Analysis and Geometry in Metric Spaces
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### Fields

 28 Potential theory (31-XX) 27 Differential geometry (53-XX) 21 Global analysis, analysis on manifolds (58-XX) 19 Functions of a complex variable (30-XX) 7 Partial differential equations (35-XX) 1 Topological groups, Lie groups (22-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX)

### Citations contained in zbMATH Open

38 Publications have been cited 487 times in 286 Documents Cited by Year
$$p$$-harmonic functions on graphs and manifolds. Zbl 0898.31007
Holopainen, Ilkka; Soardi, Paolo M.
1997
Nonlinear potential theory and quasiregular mappings on Riemannian manifolds. Zbl 0698.31010
Holopainen, Ilkka
1990
Harnack inequality and hyperbolicity for subelliptic $$p$$-Laplacians with applications to Picard type theorems. Zbl 1005.58013
Coulhon, T.; Holopainen, I.; Saloff-Coste, L.
2001
Quasiregular maps on Carnot groups. Zbl 0905.30018
Heinonen, Juha; Holopainen, Ilkka
1997
Volume growth, Green’s functions, and parabolicity of ends. Zbl 0955.31003
Holopainen, Ilkka
1999
Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups. Zbl 1014.22009
Balogh, Zoltán M.; Holopainen, Ilkka; Tyson, Jeremy T.
2002
A strong Liouville theorem for $$p$$-harmonic functions on graphs. Zbl 0874.31008
Holopainen, Ilkka; Soardi, Paolo M.
1997
Rough isometries and $$p$$-harmonic functions with finite Dirichlet integral. Zbl 0797.31008
Holopainen, Ilkka
1994
A sharp $$L^q$$-Liouville theorem for $$p$$-harmonic functions. Zbl 0955.31004
Holopainen, Ilkka
2000
Singular functions on metric measure spaces. Zbl 1039.31016
Holopainen, Ilkka; Shanmugalingam, Nageswari
2002
Quasiregular mappings, Heisenberg group, and Picard’s theorem. Zbl 0796.30018
Holopainen, I.; Rickman, S.
1993
Asymptotic Dirichlet problem for the $$p$$-Laplacian on Cartan-Hadamard manifolds. Zbl 1016.58021
Holopainen, Ilkka
2002
Asymptotic Dirichlet problem on negatively curved spaces. Zbl 1202.58017
Holopainen, Ilkka; Vähäkangas, Aleksi
2007
Positive solutions of quasilinear elliptic equations on Riemannian manifolds. Zbl 0739.53030
Holopainen, Ilkka
1992
Solutions of elliptic equations on manifolds with roughly Euclidean ends. Zbl 0833.58036
Holopainen, Ilkka
1994
Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces. Zbl 1159.53019
Holopainen, Ilkka; Lang, Urs; Vähäkangas, Aleksi
2007
Quasiregular mappings and the $$p$$-Laplace operator. Zbl 1059.30016
Holopainen, Ilkka
2003
Global comparison principles for the $$p$$-Laplace operator on Riemannian manifolds. Zbl 1222.58018
Holopainen, Ilkka; Pigola, Stefano; Veronelli, Giona
2011
Mappings of finite distortion: Global homeomorphism theorem. Zbl 1057.30020
Holopainen, Ilkka; Pankka, Pekka
2004
Volume growth and parabolicity. Zbl 0998.58024
Holopainen, Ilkka; Koskela, Pekka
2001
$$p$$-capacity and $$p$$-hyperbolicity of submanifolds. Zbl 1176.53056
Holopainen, Ilkka; Markvorsen, Steen; Palmer, Vicente
2009
Ricci curvature, Harnack functions, and Picard type theorems for quasiregular mappings. Zbl 0945.30022
Holopainen, Ilkka; Rickman, Seppo
1998
Quasiregular mappings of the Heisenberg group. Zbl 0754.30018
Holopainen, Ilkka; Rickman, Seppo
1992
A Picard type theorem for quasiregular mappings of $$\mathbb{R}^ n$$ into $$n$$- manifolds with many ends. Zbl 0763.30006
Holopainen, Ilkka; Rickman, Seppo
1992
Classification of Riemannian manifolds in nonlinear potential theory. Zbl 0771.53019
Holopainen, Ilkka; Rickman, Seppo
1993
Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds. Zbl 1330.58017
Holopainen, Ilkka; Ripoll, Jaime B.
2015
Dirichlet problem for $$f$$-minimal graphs. Zbl 1427.53079
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
2019
A big Picard theorem for quasiregular mappings into manifolds with many ends. Zbl 1068.30010
Holopainen, Ilkka; Pankka, Pekka
2005
On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold. Zbl 1380.58020
Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
2017
Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems. Zbl 1411.53027
Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
2018
On the conformal Martin boundary of domains in metric spaces. Zbl 1002.31006
Holopainen, Ilkka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2001
$$p$$-Laplace operator, quasiregular mappings and Picard-type theorems. Zbl 1161.30321
Holopainen, Ilkka; Pankka, Pekka
2007
Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures. Zbl 1372.58015
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
2017
Failure of the Denjoy theorem for quasiregular maps in dimension $$n\geq 3$$. Zbl 0854.30018
Holopainen, Ilkka; Rickman, Seppo
1996
Asymptotic Dirichlet problem for $$\mathcal{A}$$-harmonic and minimal graph equations in Cartan-Hadamard manifolds. Zbl 1430.53047
Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
2019
Nonsolvability of the asymptotic Dirichlet problem for the $$p$$-Laplacian on Cartan-Hadamard manifolds. Zbl 1342.58011
Holopainen, Ilkka
2016
Existence and non-existence of minimal graphic and $$p$$-harmonic functions. Zbl 1445.53031
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
2020
Asymptotic Dirichlet problems in warped products. Zbl 1444.58008
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka; Lira, Jorge
2020
Existence and non-existence of minimal graphic and $$p$$-harmonic functions. Zbl 1445.53031
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
2020
Asymptotic Dirichlet problems in warped products. Zbl 1444.58008
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka; Lira, Jorge
2020
Dirichlet problem for $$f$$-minimal graphs. Zbl 1427.53079
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
2019
Asymptotic Dirichlet problem for $$\mathcal{A}$$-harmonic and minimal graph equations in Cartan-Hadamard manifolds. Zbl 1430.53047
Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
2019
Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems. Zbl 1411.53027
Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
2018
On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold. Zbl 1380.58020
Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B.
2017
Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures. Zbl 1372.58015
Casteras, Jean-Baptiste; Heinonen, Esko; Holopainen, Ilkka
2017
Nonsolvability of the asymptotic Dirichlet problem for the $$p$$-Laplacian on Cartan-Hadamard manifolds. Zbl 1342.58011
Holopainen, Ilkka
2016
Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds. Zbl 1330.58017
Holopainen, Ilkka; Ripoll, Jaime B.
2015
Global comparison principles for the $$p$$-Laplace operator on Riemannian manifolds. Zbl 1222.58018
Holopainen, Ilkka; Pigola, Stefano; Veronelli, Giona
2011
$$p$$-capacity and $$p$$-hyperbolicity of submanifolds. Zbl 1176.53056
Holopainen, Ilkka; Markvorsen, Steen; Palmer, Vicente
2009
Asymptotic Dirichlet problem on negatively curved spaces. Zbl 1202.58017
Holopainen, Ilkka; Vähäkangas, Aleksi
2007
Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces. Zbl 1159.53019
Holopainen, Ilkka; Lang, Urs; Vähäkangas, Aleksi
2007
$$p$$-Laplace operator, quasiregular mappings and Picard-type theorems. Zbl 1161.30321
Holopainen, Ilkka; Pankka, Pekka
2007
A big Picard theorem for quasiregular mappings into manifolds with many ends. Zbl 1068.30010
Holopainen, Ilkka; Pankka, Pekka
2005
Mappings of finite distortion: Global homeomorphism theorem. Zbl 1057.30020
Holopainen, Ilkka; Pankka, Pekka
2004
Quasiregular mappings and the $$p$$-Laplace operator. Zbl 1059.30016
Holopainen, Ilkka
2003
Singular solutions, homogeneous norms, and quasiconformal mappings in Carnot groups. Zbl 1014.22009
Balogh, Zoltán M.; Holopainen, Ilkka; Tyson, Jeremy T.
2002
Singular functions on metric measure spaces. Zbl 1039.31016
Holopainen, Ilkka; Shanmugalingam, Nageswari
2002
Asymptotic Dirichlet problem for the $$p$$-Laplacian on Cartan-Hadamard manifolds. Zbl 1016.58021
Holopainen, Ilkka
2002
Harnack inequality and hyperbolicity for subelliptic $$p$$-Laplacians with applications to Picard type theorems. Zbl 1005.58013
Coulhon, T.; Holopainen, I.; Saloff-Coste, L.
2001
Volume growth and parabolicity. Zbl 0998.58024
Holopainen, Ilkka; Koskela, Pekka
2001
On the conformal Martin boundary of domains in metric spaces. Zbl 1002.31006
Holopainen, Ilkka; Shanmugalingam, Nageswari; Tyson, Jeremy T.
2001
A sharp $$L^q$$-Liouville theorem for $$p$$-harmonic functions. Zbl 0955.31004
Holopainen, Ilkka
2000
Volume growth, Green’s functions, and parabolicity of ends. Zbl 0955.31003
Holopainen, Ilkka
1999
Ricci curvature, Harnack functions, and Picard type theorems for quasiregular mappings. Zbl 0945.30022
Holopainen, Ilkka; Rickman, Seppo
1998
$$p$$-harmonic functions on graphs and manifolds. Zbl 0898.31007
Holopainen, Ilkka; Soardi, Paolo M.
1997
Quasiregular maps on Carnot groups. Zbl 0905.30018
Heinonen, Juha; Holopainen, Ilkka
1997
A strong Liouville theorem for $$p$$-harmonic functions on graphs. Zbl 0874.31008
Holopainen, Ilkka; Soardi, Paolo M.
1997
Failure of the Denjoy theorem for quasiregular maps in dimension $$n\geq 3$$. Zbl 0854.30018
Holopainen, Ilkka; Rickman, Seppo
1996
Rough isometries and $$p$$-harmonic functions with finite Dirichlet integral. Zbl 0797.31008
Holopainen, Ilkka
1994
Solutions of elliptic equations on manifolds with roughly Euclidean ends. Zbl 0833.58036
Holopainen, Ilkka
1994
Quasiregular mappings, Heisenberg group, and Picard’s theorem. Zbl 0796.30018
Holopainen, I.; Rickman, S.
1993
Classification of Riemannian manifolds in nonlinear potential theory. Zbl 0771.53019
Holopainen, Ilkka; Rickman, Seppo
1993
Positive solutions of quasilinear elliptic equations on Riemannian manifolds. Zbl 0739.53030
Holopainen, Ilkka
1992
Quasiregular mappings of the Heisenberg group. Zbl 0754.30018
Holopainen, Ilkka; Rickman, Seppo
1992
A Picard type theorem for quasiregular mappings of $$\mathbb{R}^ n$$ into $$n$$- manifolds with many ends. Zbl 0763.30006
Holopainen, Ilkka; Rickman, Seppo
1992
Nonlinear potential theory and quasiregular mappings on Riemannian manifolds. Zbl 0698.31010
Holopainen, Ilkka
1990
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### Cited by 294 Authors

 19 Holopainen, Ilkka 11 Shanmugalingam, Nageswari 10 Björn, Anders 10 Björn, Jana 10 Pankka, Pekka 10 Rodríguez García, José Manuel 9 Touris, Eva 8 Castéras, Jean-baptiste 8 Portilla, Ana 8 Rigoli, Marco 7 Adamowicz, Tomasz 7 Pigola, Stefano 6 Heinonen, Esko 6 Setti, Alberto G. 5 Chung, Soon-Yeong 5 Hua, Bobo 5 Koskela, Pekka 5 Palmer, Vicente 5 Ripoll, Jaime Bruck 5 Veronelli, Giona 4 Bieske, Thomas J. 4 D’Ambrosio, Lorenzo 4 Jost, Jürgen 4 Markina, Irina 4 Marola, Niko 4 Puls, Michael J. 4 Rajala, Kai 4 Troyanov, Marc 4 Vodop’yanov, Sergeĭ Konstantinovich 3 Capogna, Luca 3 Enciso, Alberto 3 Garofalo, Nicola 3 Goldstein, Jerome Arthur 3 Granados, Ana 3 Kasue, Atsushi 3 Kinnunen, Juha 3 Kombe, Ismail 3 Lee, Paul W. Y. 3 Lee, Yong Hah 3 Lehrbäck, Juha 3 Mari, Luciano 3 Markvorsen, Steen 3 Nguyen Cong Phuc 3 Onninen, Jani 3 Park, Jea-Hyun 3 Peralta-Salas, Daniel 3 Salvatori, Maura 3 Tyson, Jeremy T. 3 Vignati, Marco 3 Wu, Qingyan 2 Aikawa, Hiroaki 2 Andrade, Maria Gorete C. 2 Balogh, Zoltán M. 2 Cowling, Michael G. 2 Dairbekov, Nurlan Slyamkhanovich 2 Danielli, Donatella 2 Dinh, Si Tiep 2 Drasin, David 2 Fässler, Katrin S. 2 Gao, Qiang 2 Gol’dshtein, Vladimir Mikhailovich 2 Gournay, Antoine 2 Grigor’yan, Alexander Asaturovich 2 Hattori, Tae 2 Heinonen, Juha 2 Hencl, Stanislav 2 Hurtado, Ana 2 Keller, Matthias 2 Kilpeläinen, Tero 2 Kim, Soojung 2 Kurdyka, Krzysztof 2 Lang, Urs 2 Lin, Yong 2 Luisto, Rami 2 Magliaro, Marco 2 Manfredi, Juan J. 2 Martio, Olli 2 Mramor, Blaz 2 Mugnai, Dimitri 2 Mugnolo, Delio 2 Nguyen, Khanh Ngoc 2 Nyström, Kaj 2 Okuyama, Yûsuke 2 Peltonen, Kirsi 2 Pestana, Domingo 2 Pucci, Patrizia 2 Rickman, Seppo Uolevi 2 Sevost’yanov, Yevgen Oleksandrovych 2 Sudoplatov, Sergeĭ Vladimirovich 2 Sun, Yuhua 2 Telichevesky, Miriam 2 Tessera, Romain 2 Tetenov, Andreĭ Viktorovich 2 Ukhlov, Alexander Dadar-Oolovich 2 Vähäkangas, Aleksi 2 Valtorta, Daniele 2 Wang, Wei 2 Wang, Zhuang 2 Warhurst, Ben 2 Yan, Baisheng ...and 194 more Authors
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### Cited in 96 Serials

 29 Sibirskie Èlektronnye Matematicheskie Izvestiya 18 Potential Analysis 14 Journal of Mathematical Analysis and Applications 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 11 Mathematische Zeitschrift 10 Mathematische Annalen 9 Proceedings of the American Mathematical Society 9 The Journal of Geometric Analysis 7 Transactions of the American Mathematical Society 6 Advances in Mathematics 6 Journal of Differential Equations 6 Journal of Functional Analysis 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Siberian Mathematical Journal 5 Revista Matemática Iberoamericana 4 Israel Journal of Mathematics 4 Journal d’Analyse Mathématique 4 Annales de l’Institut Fourier 4 Calculus of Variations and Partial Differential Equations 4 Acta Mathematica Sinica. English Series 3 Communications on Pure and Applied Mathematics 3 Arkiv för Matematik 3 Acta Mathematica 3 Duke Mathematical Journal 3 Geometriae Dedicata 3 Annals of Global Analysis and Geometry 3 Annales Academiae Scientiarum Fennicae. Mathematica 3 Revista Matemática Complutense 3 Analysis and Geometry in Metric Spaces 2 Manuscripta Mathematica 2 Michigan Mathematical Journal 2 Nagoya Mathematical Journal 2 Proceedings of the Japan Academy. Series A 2 Results in Mathematics 2 Tohoku Mathematical Journal. Second Series 2 Discrete & Computational Geometry 2 International Journal of Mathematics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Bulletin des Sciences Mathématiques 2 Journal of Difference Equations and Applications 2 Discrete and Continuous Dynamical Systems 2 Conformal Geometry and Dynamics 2 Communications on Pure and Applied Analysis 2 Analysis and Mathematical Physics 2 Annales Fennici Mathematici 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Computers & Mathematics with Applications 1 Discrete Applied Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry and Physics 1 American Journal of Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Czechoslovak Mathematical Journal 1 Functional Analysis and its Applications 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Journal of Geometry 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Kodai Mathematical Journal 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Ricerche di Matematica 1 Bulletin of the Korean Mathematical Society 1 Combinatorica 1 Acta Mathematica Hungarica 1 Forum Mathematicum 1 Science in China. Series A 1 Differential Geometry and its Applications 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Applied Mathematics. Series B (English Edition) 1 Journal of Mathematical Sciences (New York) 1 Sbornik: Mathematics 1 Journal of Dynamical and Control Systems 1 Communications in Contemporary Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Advanced Nonlinear Studies 1 Computational Methods and Function Theory 1 Milan Journal of Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Complex Analysis and Operator Theory 1 Journal of Topology and Analysis 1 Science China. Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Advances in Nonlinear Analysis 1 Complex Analysis and its Synergies
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### Cited in 43 Fields

 86 Differential geometry (53-XX) 84 Potential theory (31-XX) 80 Partial differential equations (35-XX) 78 Functions of a complex variable (30-XX) 64 Global analysis, analysis on manifolds (58-XX) 27 Functional analysis (46-XX) 20 Combinatorics (05-XX) 18 Abstract harmonic analysis (43-XX) 17 Real functions (26-XX) 16 Topological groups, Lie groups (22-XX) 10 Group theory and generalizations (20-XX) 9 Probability theory and stochastic processes (60-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 5 Measure and integration (28-XX) 5 Difference and functional equations (39-XX) 5 Operator theory (47-XX) 5 General topology (54-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Convex and discrete geometry (52-XX) 3 History and biography (01-XX) 3 Mathematical logic and foundations (03-XX) 3 Ordinary differential equations (34-XX) 3 Manifolds and cell complexes (57-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 General algebraic systems (08-XX) 2 Algebraic geometry (14-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Geometry (51-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 2 Mechanics of particles and systems (70-XX) 2 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Mathematics education (97-XX)