# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 34 Publications since 1966, including 4 Books
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#### Co-Authors

 23 single-authored 4 Fournier, John J. F. 2 Aronszajn, Nachman 1 Clarke, Francis H. 1 Fleming, Richard A. 1 Hanna, Martin S. 1 Sandretto, Carmen 1 Smith, Kennan T.
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#### Serials

 6 Canadian Mathematical Bulletin 4 Journal of Mathematical Analysis and Applications 3 Canadian Journal of Mathematics 2 Annales de l’Institut Fourier 2 Journal of Functional Analysis 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 1 Archive for Rational Mechanics and Analysis 1 American Journal of Mathematics 1 Časopis Pro Pěstování Matematiky 1 Journal of Differential Equations 1 Journal of Optimization Theory and Applications 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Natural Resource Modeling 1 Journal of Mathematics and Mechanics
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#### Fields

 15 Functional analysis (46-XX) 5 Real functions (26-XX) 2 General and overarching topics; collections (00-XX) 2 Potential theory (31-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

28 Publications have been cited 5,408 times in 5,242 Documents Cited by Year
Sobolev spaces. Zbl 0314.46030
1975
Sobolev spaces. 2nd ed. Zbl 1098.46001
Adams, Robert A.; Fournier, John J. F.
2003
Equivalent norms for Sobolev spaces. Zbl 0186.19101
1970
Real interpolation of Sobolev spaces on subdomains of $$R^N$$. Zbl 0347.46040
Adams, R. A.; Fournier, J. J. F.
1978
Cone conditions and properties of Sobolev spaces. Zbl 0385.46024
1977
Theory of Bessel potentials. II. Zbl 0185.19703
Adams, Robert; Aronszajn, Nachman; Smith, K. T.
1967
On the Orlicz-Sobolev imbedding theorem. Zbl 0344.46077
1977
General logarithmic Sobolev inequalities and Orlicz imbeddings. Zbl 0425.46020
1979
Some imbedding theorems for Sobolev spaces. Zbl 0201.16301
1971
The uniform continuity of functions in Sobolev spaces. Zbl 0339.46027
1976
Gross’ logarithmic Sobolev inequality: A simple proof. Zbl 0421.46029
Adams, R. A.; Clarke, Frank H.
1979
Compact imbeddings of weighted Sobolev spaces on unbounded domains. Zbl 0209.15004
1971
Some integral inequalities with applications to the imbedding of Sobolev spaces defined over irregular domains. Zbl 0262.46036
1973
Capacity and compact imbeddings. Zbl 0193.41402
1970
Compact Sobolev imbeddings for unbounded domains with discrete boundaries. Zbl 0209.15003
1968
The Rellich-Kondrachov theorem for unbounded domains. Zbl 0157.20401
1968
Theory of Bessel potentials. III: Potentials on regular manifolds. Zbl 0176.09902
Adams, Robert; Aronszajn, Nachman; Hanna, M. S.
1969
Calculus: a complete course. 4th ed. Zbl 0943.26002
1999
Compact Sobolev imbeddings for unbounded domains. Zbl 0187.37704
1970
Reduced Sobolev inequalities. Zbl 0662.46036
1988
Anisotropic Sobolev inequalities. Zbl 0663.46024
1988
A compact imbedding theorem for functions without compact support. Zbl 0219.46031
1971
An alternative specification for modeling groundwater dynamics. Zbl 0927.91032
Kim, C. S.; Sandretto, C.; Fleming, R. A.; Adams, R. A.
1997
Direct solution of an optimal layout problem for isotropic heat conductors with a volume fraction constraint. Zbl 0832.49004
1995
Compact Sobolev imbeddings for pepper sets. Zbl 0176.43401
1969
$$-\Delta$$ is positive definite on a ’spiny urchin’. Zbl 0176.45101
1969
Compact imbedding theorems for quasibounded domains. Zbl 0194.43801
1970
An intrinsic approach to radiation conditions. Zbl 0241.35018
Roach, G. F.; Adams, R. A.
1972
Sobolev spaces. 2nd ed. Zbl 1098.46001
Adams, Robert A.; Fournier, John J. F.
2003
Calculus: a complete course. 4th ed. Zbl 0943.26002
1999
An alternative specification for modeling groundwater dynamics. Zbl 0927.91032
Kim, C. S.; Sandretto, C.; Fleming, R. A.; Adams, R. A.
1997
Direct solution of an optimal layout problem for isotropic heat conductors with a volume fraction constraint. Zbl 0832.49004
1995
Reduced Sobolev inequalities. Zbl 0662.46036
1988
Anisotropic Sobolev inequalities. Zbl 0663.46024
1988
General logarithmic Sobolev inequalities and Orlicz imbeddings. Zbl 0425.46020
1979
Gross’ logarithmic Sobolev inequality: A simple proof. Zbl 0421.46029
Adams, R. A.; Clarke, Frank H.
1979
Real interpolation of Sobolev spaces on subdomains of $$R^N$$. Zbl 0347.46040
Adams, R. A.; Fournier, J. J. F.
1978
Cone conditions and properties of Sobolev spaces. Zbl 0385.46024
1977
On the Orlicz-Sobolev imbedding theorem. Zbl 0344.46077
1977
The uniform continuity of functions in Sobolev spaces. Zbl 0339.46027
1976
Sobolev spaces. Zbl 0314.46030
1975
Some integral inequalities with applications to the imbedding of Sobolev spaces defined over irregular domains. Zbl 0262.46036
1973
An intrinsic approach to radiation conditions. Zbl 0241.35018
Roach, G. F.; Adams, R. A.
1972
Some imbedding theorems for Sobolev spaces. Zbl 0201.16301
1971
Compact imbeddings of weighted Sobolev spaces on unbounded domains. Zbl 0209.15004
1971
A compact imbedding theorem for functions without compact support. Zbl 0219.46031
1971
Equivalent norms for Sobolev spaces. Zbl 0186.19101
1970
Capacity and compact imbeddings. Zbl 0193.41402
1970
Compact Sobolev imbeddings for unbounded domains. Zbl 0187.37704
1970
Compact imbedding theorems for quasibounded domains. Zbl 0194.43801
1970
Theory of Bessel potentials. III: Potentials on regular manifolds. Zbl 0176.09902
Adams, Robert; Aronszajn, Nachman; Hanna, M. S.
1969
Compact Sobolev imbeddings for pepper sets. Zbl 0176.43401
1969
$$-\Delta$$ is positive definite on a ’spiny urchin’. Zbl 0176.45101
1969
Compact Sobolev imbeddings for unbounded domains with discrete boundaries. Zbl 0209.15003
1968
The Rellich-Kondrachov theorem for unbounded domains. Zbl 0157.20401
1968
Theory of Bessel potentials. II. Zbl 0185.19703
Adams, Robert; Aronszajn, Nachman; Smith, K. T.
1967
all top 5

#### Cited by 5,906 Authors

 35 He, Yinnian 31 Wang, Hong 28 Luo, Zhendong 26 Kweon, Jae Ryong 25 Fuchs, Martin 25 Oden, John Tinsley 24 Ciarlet, Philippe Gaston 24 Yao, Fengping 22 Ruas, Vitoriano 21 Girault, Vivette 21 Mardare, Cristinel 21 Shang, Yueqiang 20 Gunzburger, Max D. 19 Li, Jian 19 Zheng, Xiangcheng 18 Rădulescu, Vicenţiu D. 18 Zhou, Aihui 16 Wheeler, Mary Fanett 16 Yang, Danping 15 Brenner, Susanne Cecelia 15 Byun, Sun-Sig 15 Fan, Jishan 15 Guo, Ben-Yu 14 Amrouche, Chérif 14 Bildhauer, Michael 14 Hild, Patrick 14 Li, Hong 14 Zhao, Caidi 13 Huang, Jianguo 13 Mingione, Giuseppe 13 Quarteroni, Alfio M. 13 Saanouni, Tarek 13 Sun, Shuyu 13 Weder, Ricardo A. 13 Zhou, Shengfan 12 Benkirane, Abdelmoujib 12 Bernardi, Christine 12 Cianchi, Andrea 12 Gatica, Gabriel N. 12 Hintermüller, Michael 12 Jiang, Song 12 Li, Buyang 12 Manservisi, Sandro 12 Novo, Julia 12 Vuillermot, Pierre-A. 12 Zhao, Peihao 11 Alves, Claudianor Oliveira 11 Chen, Zhangxin 11 Guo, Hui 11 Mihăilescu, Mihai 11 Papageorgiou, Nikolaos S. 11 Shi, Dongyang 11 Van Schaftingen, Jean 11 White, Luther W. 11 Xie, Hehu 10 Balachandran, Krishnan 10 Ben Belgacem, Faker 10 Breit, Dominic 10 Deka, Bhupen 10 Du, Qiang 10 Duan, Huoyuan 10 Feehan, Paul M. N. 10 Feng, Xiaobing 10 Górka, Przemysław 10 Maday, Yvon 10 Melenk, Jens Markus 10 Ming, Pingbing 10 Renard, Yves 10 Xu, Jinchao 10 Zheng, Haibiao 9 Barbu, Viorel 9 Belmiloudi, Aziz 9 Chen, Yanping 9 Chentouf, Boumediène 9 Dutra do Carmo, Eduardo Gomes 9 Fan, Xianling 9 García-Archilla, Bosco 9 Gupur, Geni 9 Han, Houde 9 Hou, Yanren 9 Jin, Bangti 9 Luskin, Mitchell 9 Nicaise, Serge 9 Pucci, Patrizia 9 Rui, Hongxing 9 Sayas, Francisco-Javier 9 Shi, Zhongci 9 Sweers, Guido H. 9 Teng, Fei 9 Titi, Edriss Saleh 9 Verfürth, Rüdiger 9 Wendland, Wolfgang L. 9 Yamamoto, Masahiro 9 Yeh, Li-Ming 9 Zhang, Jiansong 9 Zhou, Shulin 8 Abdellaoui, Boumediene 8 An, Rong 8 Arcangeli, Remi 8 Bao, Weizhu ...and 5,806 more Authors
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#### Cited in 464 Serials

 417 Journal of Mathematical Analysis and Applications 238 Journal of Differential Equations 181 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 151 Journal of Computational and Applied Mathematics 138 Computer Methods in Applied Mechanics and Engineering 136 Numerische Mathematik 133 Applied Mathematics and Computation 128 Computers & Mathematics with Applications 113 Journal of Functional Analysis 105 Nonlinear Analysis. Theory, Methods & Applications 96 Applied Numerical Mathematics 93 Journal of Scientific Computing 84 Mathematics of Computation 82 Mathematical Methods in the Applied Sciences 81 Archive for Rational Mechanics and Analysis 70 Transactions of the American Mathematical Society 68 Communications in Mathematical Physics 59 Calculus of Variations and Partial Differential Equations 54 Journal of Computational Physics 47 Nonlinear Analysis. Real World Applications 46 Journal de Mathématiques Pures et Appliquées. Neuvième Série 45 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 43 Numerical Methods for Partial Differential Equations 41 Mathematische Nachrichten 40 Annali di Matematica Pura ed Applicata. Serie Quarta 40 Journal of Approximation Theory 40 Mathematische Annalen 38 ZAMP. Zeitschrift für angewandte Mathematik und Physik 36 Proceedings of the American Mathematical Society 34 Discrete and Continuous Dynamical Systems 34 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 33 Boundary Value Problems 32 Mathematische Zeitschrift 32 RAIRO. Modélisation Mathématique et Analyse Numérique 32 Journal of Mathematical Fluid Mechanics 31 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 30 Applied Mathematics and Optimization 29 Zeitschrift für Analysis und ihre Anwendungen 29 Comptes Rendus. Mathématique. Académie des Sciences, Paris 28 Applied Mathematics Letters 28 Potential Analysis 28 NoDEA. Nonlinear Differential Equations and Applications 27 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 27 Acta Mathematica Sinica. English Series 25 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 25 Acta Applicandae Mathematicae 24 Advances in Computational Mathematics 23 Applicable Analysis 23 Automatica 23 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 22 International Journal of Engineering Science 22 Manuscripta Mathematica 20 Mathematical and Computer Modelling 20 Communications in Partial Differential Equations 19 Rocky Mountain Journal of Mathematics 19 Stochastic Processes and their Applications 19 Journal of Evolution Equations 18 Discrete and Continuous Dynamical Systems. Series B 17 Advances in Mathematics 17 SIAM Journal on Numerical Analysis 17 Journal of Elasticity 17 Journal of Inequalities and Applications 16 Calcolo 16 SIAM Journal on Mathematical Analysis 16 Communications on Pure and Applied Analysis 16 Science China. Mathematics 15 Rendiconti del Seminario Matematico della Università di Padova 15 Probability Theory and Related Fields 15 Journal of Complexity 15 Annales Henri Poincaré 14 Journal of Mathematical Physics 14 Journal of Optimization Theory and Applications 14 Acta Mathematicae Applicatae Sinica. English Series 14 Applications of Mathematics 14 Applied and Computational Harmonic Analysis 14 Lobachevskii Journal of Mathematics 14 Mediterranean Journal of Mathematics 14 Journal of Elliptic and Parabolic Equations 13 The Annals of Probability 13 Integral Equations and Operator Theory 13 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 13 Physica D 13 Numerical Algorithms 13 Applied Mathematical Modelling 13 SIAM Journal on Scientific Computing 12 Computing 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Journal of the European Mathematical Society (JEMS) 12 Journal of Applied Mathematics and Computing 11 Communications on Pure and Applied Mathematics 11 BIT 11 Czechoslovak Mathematical Journal 11 International Journal for Numerical Methods in Engineering 11 The Journal of Fourier Analysis and Applications 11 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 10 Mathematics and Computers in Simulation 10 Numerical Functional Analysis and Optimization 10 Journal of Integral Equations and Applications 10 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 10 Journal of Dynamics and Differential Equations ...and 364 more Serials
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#### Cited in 55 Fields

 3,101 Partial differential equations (35-XX) 1,461 Numerical analysis (65-XX) 944 Fluid mechanics (76-XX) 569 Functional analysis (46-XX) 553 Calculus of variations and optimal control; optimization (49-XX) 551 Mechanics of deformable solids (74-XX) 432 Operator theory (47-XX) 250 Probability theory and stochastic processes (60-XX) 195 Ordinary differential equations (34-XX) 177 Global analysis, analysis on manifolds (58-XX) 158 Biology and other natural sciences (92-XX) 155 Systems theory; control (93-XX) 132 Real functions (26-XX) 130 Approximations and expansions (41-XX) 123 Quantum theory (81-XX) 116 Statistical mechanics, structure of matter (82-XX) 114 Optics, electromagnetic theory (78-XX) 112 Integral equations (45-XX) 108 Harmonic analysis on Euclidean spaces (42-XX) 101 Differential geometry (53-XX) 94 Dynamical systems and ergodic theory (37-XX) 88 Statistics (62-XX) 81 Classical thermodynamics, heat transfer (80-XX) 63 Potential theory (31-XX) 56 Operations research, mathematical programming (90-XX) 52 Computer science (68-XX) 49 Information and communication theory, circuits (94-XX) 42 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 40 Geophysics (86-XX) 39 Mechanics of particles and systems (70-XX) 35 Functions of a complex variable (30-XX) 34 Several complex variables and analytic spaces (32-XX) 28 Relativity and gravitational theory (83-XX) 21 Measure and integration (28-XX) 21 Manifolds and cell complexes (57-XX) 19 Special functions (33-XX) 12 Integral transforms, operational calculus (44-XX) 12 General topology (54-XX) 11 Algebraic topology (55-XX) 9 Topological groups, Lie groups (22-XX) 9 Difference and functional equations (39-XX) 9 Abstract harmonic analysis (43-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 5 Mathematical logic and foundations (03-XX) 5 Astronomy and astrophysics (85-XX) 4 History and biography (01-XX) 4 Combinatorics (05-XX) 3 General and overarching topics; collections (00-XX) 3 Number theory (11-XX) 3 Algebraic geometry (14-XX) 3 Convex and discrete geometry (52-XX) 2 Category theory; homological algebra (18-XX) 1 Associative rings and algebras (16-XX) 1 Sequences, series, summability (40-XX) 1 Geometry (51-XX)