Åhag, Per; Czyż, Rafał; Lu, Chinh H.; Rashkovskii, Alexander Kiselman minimum principle and rooftop envelopes in complex Hessian equations. (English) Zbl 07941236 Math. Z. 308, No. 4, Paper No. 70, 24 p. (2024). MSC: 32U05 32U35 32W20 32F17 53C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Arendt, W.; ter Elst, A. F. M.; Sauter, M. The Perron solution for elliptic equations without the maximum principle. (English) Zbl 07932322 Math. Ann. 390, No. 1, 763-810 (2024). Reviewer: Peter Lindqvist (Trondheim) MSC: 31B25 35J25 46E35 31C25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gushchin, A. K. On Dirichlet problem. (English. Russian original) Zbl 1533.35070 Theor. Math. Phys. 218, No. 1, 51-67 (2024); translation from Teor. Mat. Fiz. 218, No. 1, 60-79 (2024). MSC: 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Benyaiche, Allami; Khlifi, Ismail PWB-method and Wiener criterion for boundary regularity under generalized Orlicz growth. (English) Zbl 1517.35110 Positivity 27, No. 2, Paper No. 24, 31 p. (2023). MSC: 35J62 35J25 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anghel, Cipriana; Stan, Rareş Uniformization of Riemann surfaces revisited. (English) Zbl 1502.30121 Ann. Global Anal. Geom. 62, No. 3, 603-615 (2022). MSC: 30F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Björn, Anders; Hansevi, Daniel Semiregular and strongly irregular boundary points for \(p\)-harmonic functions on unbounded sets in metric spaces. (English) Zbl 1494.31023 Collect. Math. 73, No. 2, 253-270 (2022). MSC: 31E05 30L99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Björn, Anders; Björn, Jana; Mwasa, Abubakar Resolutivity and invariance for the Perron method for degenerate equations of divergence type. (English) Zbl 1483.35097 J. Math. Anal. Appl. 509, No. 1, Article ID 125937, 14 p. (2022). MSC: 35J70 35J62 35J25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Di Biase, Fausto; Krantz, Steven G. Foundations of Fatou theory and a tribute to the work of E. M. Stein on boundary behavior of holomorphic functions. (English) Zbl 1477.32013 J. Geom. Anal. 31, No. 7, 7184-7296 (2021). MSC: 32A40 31B25 32A35 28A15 × Cite Format Result Cite Review PDF Full Text: DOI
Kasue, Atsushi Resolutive ideal boundaries of nonlinear resistive networks. (English) Zbl 1436.31028 Positivity 24, No. 1, 151-196 (2020). MSC: 31C20 05C63 × Cite Format Result Cite Review PDF Full Text: DOI
Alkhutov, Yu. A.; Surnachev, M. D. Behavior of solutions of the Dirichlet problem for the \(p(x)\)-Laplacian at a boundary point. (English. Russian original) Zbl 1437.35401 St. Petersbg. Math. J. 31, No. 2, 251-271 (2020); translation from Algebra Anal. 31, No. 2, 88-117 (2019). MSC: 35J92 35J25 35B65 × Cite Format Result Cite Review PDF Full Text: DOI
Björn, Anders; Hansevi, Daniel Boundary regularity for p-harmonic functions and solutions of obstacle problems on unbounded sets in metric spaces. (English) Zbl 1436.31032 Anal. Geom. Metr. Spaces 7, 179-196 (2019). MSC: 31E05 30L99 35J66 35J92 49Q20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ross, Julius; Witt Nyström, David The Dirichlet problem for the complex homogeneous Monge-Ampère equation. (English) Zbl 1448.32004 Muñoz, Vicente (ed.) et al., Modern geometry. A celebration of the work of Simon Donaldson. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 99, 289-330 (2018). MSC: 32W20 35J96 53E30 32Q15 58J32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Berchenko-Kogan, Yakov Yang-Mills replacement. (English) Zbl 1406.58008 J. Geom. Anal. 28, No. 4, 3603-3656 (2018). MSC: 58E15 58E20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Åhag, Per; Czyż, Rafał; Hed, Lisa The geometry of \(m\)-hyperconvex domains. (English) Zbl 1421.31016 J. Geom. Anal. 28, No. 4, 3196-3222 (2018). Reviewer: Marek Jarnicki (Kraków) MSC: 31C05 32F17 32U05 31B25 32U10 32T35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bulíček, Miroslav; Maringová, Erika; Stroffolini, Bianca; Verde, Anna A boundary regularity result for minimizers of variational integrals with nonstandard growth. (English) Zbl 1402.35099 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 177, Part A, 153-168 (2018). MSC: 35J25 35J20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alkhutov, Yuriĭ A.; Surnachev, M. D. Regularity of a boundary point for the \(p(x)\)-Laplacian. (English. Russian original) Zbl 1400.35143 J. Math. Sci., New York 232, No. 3, 206-231 (2018); translation from Probl. Mat. Anal. 92, No. 3, 5-25 (2018). MSC: 35J92 35J40 × Cite Format Result Cite Review PDF Full Text: DOI
Hansevi, Daniel The Perron method for \(p\)-harmonic functions in unbounded sets in \(\mathbf {R}^n\) and metric spaces. (English) Zbl 1397.31004 Math. Z. 288, No. 1-2, 55-74 (2018). Reviewer: Giovanni Anello (Messina) MSC: 31E05 31C45 × Cite Format Result Cite Review PDF Full Text: DOI
Ismaeel, Tariq On the Wiener criterion in higher dimensions. (English) Zbl 1386.35002 Bound. Value Probl. 2017, Paper No. 174, 5 p. (2017). MSC: 35A01 35B65 35J05 35J25 × Cite Format Result Cite Review PDF Full Text: DOI
Lindgren, Erik; Lindqvist, Peter Perron’s method and Wiener’s theorem for a nonlocal equation. (English) Zbl 1378.35124 Potential Anal. 46, No. 4, 705-737 (2017). Reviewer: Andrei Perjan (Chişinău) MSC: 35J60 35R11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Greene, Robert E.; Kim, Kang-Tae The Riemann mapping theorem from Riemann’s viewpoint. (English) Zbl 1361.30015 Complex Anal. Synerg. 3, Paper No. 1, 11 p. (2017). MSC: 30C35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kinnunen, Juha; Lindqvist, Peter; Lukkari, Teemu Perron’s method for the porous medium equation. (English) Zbl 1361.35079 J. Eur. Math. Soc. (JEMS) 18, No. 12, 2953-2969 (2016). MSC: 35K55 35K65 35K20 31C45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Greco, Gabriele H.; Mazzucchi, Sonia Peano’s 1886 existence theorem on first-order scalar differential equations: a review. (English) Zbl 1354.01011 Boll. Unione Mat. Ital. 9, No. 3, 375-389 (2016). Reviewer: Davide Bondoni (Anfo) MSC: 01A55 34-03 34A12 34A40 × Cite Format Result Cite Review PDF Full Text: DOI
Talib, Imran; Asif, Naseer Ahmad; Tunc, Cemil Coupled lower and upper solution approach for the existence of solutions of nonlinear coupled system with nonlinear coupled boundary conditions. (English) Zbl 1343.34061 Proyecciones 35, No. 1, 99-117 (2016). MSC: 34B15 47N20 × Cite Format Result Cite Review PDF Full Text: DOI
Gushchin, A. K. On the Dirichlet problem for an elliptic equation. (Russian. English summary) Zbl 1413.35163 Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki 19, No. 1, 19-43 (2015). MSC: 35J25 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Gushchin, A. K. V. A. Steklov’s work on equations of mathematical physics and development of his results in this field. (English. Russian original) Zbl 1339.35204 Proc. Steklov Inst. Math. 289, 134-151 (2015); translation from Tr. Mat. Inst. Steklova 289, 145-162 (2015). MSC: 35Qxx 35-03 01A70 01A60 × Cite Format Result Cite Review PDF Full Text: DOI
Gushchin, A. K. Solvability of the Dirichlet problem for an inhomogeneous second-order elliptic equation. (English. Russian original) Zbl 1333.35035 Sb. Math. 206, No. 10, 1410-1439 (2015); translation from Mat. Sb. 206, No. 10, 71-102 (2015). MSC: 35J25 35J67 × Cite Format Result Cite Review PDF Full Text: DOI
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari The Dirichlet problem for \(p\)-harmonic functions with respect to the Mazurkiewicz boundary, and new capacities. (English) Zbl 1341.31009 J. Differ. Equations 259, No. 7, 3078-3114 (2015). Reviewer: Haibo Lin (Beijing) MSC: 31E05 30L99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Björn, Anders; Björn, Jana; Gianazza, Ugo; Parviainen, Mikko Boundary regularity for degenerate and singular parabolic equations. (English) Zbl 1333.35087 Calc. Var. Partial Differ. Equ. 52, No. 3-4, 797-827 (2015). Reviewer: Peter Lindqvist (Trondheim) MSC: 35K20 31B25 35B65 35K65 35K67 35K92 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Björn, Anders The Dirichlet problem for \(p\)-harmonic functions on the topologist’s comb. (English) Zbl 1308.31008 Math. Z. 279, No. 1-2, 389-405 (2015). Reviewer: Marius Ghergu (Dublin) MSC: 31B30 31C45 35J66 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Adamowicz, Tomasz; Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari Prime ends for domains in metric spaces. (English) Zbl 1297.30056 Adv. Math. 238, 459-505 (2013). Reviewer: K. T. Hallenbeck (Chester) MSC: 30D40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Di Biase, Fausto On the boundary behavior of holomorphic and harmonic functions. (English) Zbl 1266.30023 Picardello, Massimo A. (ed.), Trends in harmonic analysis. Selected papers of the conference on harmonic analysis, Rome, Italy, May 30–June 4, 2011. Berlin: Springer (ISBN 978-88-470-2852-4/hbk; 978-88-470-2853-1/ebook). Springer INdAM Series 3, 207-244 (2013). MSC: 30E25 31A20 30H10 30J99 × Cite Format Result Cite Review PDF Full Text: DOI
Yuan, Zixia; Yuan, Guanxiu Dirichlet problems for linear and semilinear sub-Laplace equations on Carnot groups. (English) Zbl 1279.35024 J. Inequal. Appl. 2012, Paper No. 136, 12 p. (2012). MSC: 35J25 35J70 35J60 × Cite Format Result Cite Review PDF Full Text: DOI
König, Manfred On J. Schauder’s method to solve elliptic differential equations. (English) Zbl 1241.35090 J. Fixed Point Theory Appl. 9, No. 2, 135-196 (2011). Reviewer: Marius Ghergu (Dublin) MSC: 35J62 35J66 35J25 35A09 35B65 35B45 × Cite Format Result Cite Review PDF Full Text: DOI
Kaiser, Tobias Dirichlet regularity of subanalytic domains. (English) Zbl 1159.31002 Trans. Am. Math. Soc. 360, No. 12, 6573-6594 (2008). Reviewer: Juhani Riihentaus (Joensuu) MSC: 31B25 32B20 03C64 × Cite Format Result Cite Review PDF Full Text: DOI
van der Walt, Jan Harm The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives. (English) Zbl 1154.35328 Acta Appl. Math. 103, No. 1, 1-17 (2008). MSC: 35G20 54A20 06B30 46E05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lins Neto, A.; Canille Martins, J. C. Hermitian metrics inducing the Poincaré metric, in the leaves of a singular holomorphic foliation by curves. (English) Zbl 1069.37039 Trans. Am. Math. Soc. 356, No. 7, 2963-2988 (2004). Reviewer: Pei-Chu Hu (Jinan) MSC: 37F75 32S65 × Cite Format Result Cite Review PDF Full Text: DOI
Björn, Anders; Björn, Jana; Shanmugalingam, Nageswari The Perron method for \(p\)-harmonic functions in metric spaces. (English) Zbl 1039.35033 J. Differ. Equations 195, No. 2, 398-429 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35J60 31C45 46E35 × Cite Format Result Cite Review PDF Full Text: DOI
Krutitskii, P. A. The integral representation for a solution of the 2-D Dirichlet problem with boundary data on closed and open curves. (English) Zbl 1129.35342 Mathematika 47, No. 1-2, 339-354 (2000). MSC: 35J25 35C15 31A25 45B05 × Cite Format Result Cite Review PDF Full Text: DOI
Brézis, Haïm; Browder, Felix Partial differential equations in the 20th century. (English) Zbl 0915.01011 Adv. Math. 135, No. 1, 76-144 (1998). Reviewer: S.D.Chatterji (Lausanne) MSC: 01A60 35-02 × Cite Format Result Cite Review PDF Full Text: DOI Backlinks: MO
Ishii, Hitoshi Perron’s method for Hamilton-Jacobi equations. (English) Zbl 0697.35030 Duke Math. J. 55, 369-384 (1987). Reviewer: J.-H.Tian MSC: 35F30 70H20 35B50 × Cite Format Result Cite Review PDF Full Text: DOI
Lieberman, Gary M. Mixed boundary value problems for elliptic and parabolic differential equations of second order. (English) Zbl 0609.35021 J. Math. Anal. Appl. 113, 422-440 (1986). Reviewer: G.Perla Menzala MSC: 35G15 35K20 35J25 35A05 35B65 × Cite Format Result Cite Review PDF Full Text: DOI
Lieberman, Gary M. The Perron process applied to oblique derivative problems. (English) Zbl 0567.35027 Adv. Math. 55, 161-172 (1985). Reviewer: M.Wiegner MSC: 35J25 35A05 × Cite Format Result Cite Review PDF Full Text: DOI
Synowiec, John Distributions: The evolution of a mathematical theory. (English) Zbl 0513.01006 Hist. Math. 10, 149-183 (1983). MSC: 01A60 35-03 44-03 × Cite Format Result Cite Review PDF Full Text: DOI
Frank, Evelyn Oskar Perron (1880–1975). (English) Zbl 0479.01022 J. Number Theory 14, 281-291 (1982). MSC: 01A70 × Cite Format Result Cite Review PDF Full Text: DOI
Gårding, Lars The Dirichlet problem. (English) Zbl 0437.35025 Math. Intell. 2, 43-53 (1979). MSC: 35J05 35-01 01A99 31C05 31B05 31C25 × Cite Format Result Cite Review PDF Full Text: DOI
König, Manfred Über das Verhalten der Lösung des Dirichletproblems am Rand des Gebietes, wenn der Rand zur Klasse \(C^{2,\alpha}\) gehört. (German) Zbl 0402.35035 Proc. R. Soc. Edinb., Sect. A 80, 163-176 (1978). MSC: 35J25 35B30 × Cite Format Result Cite Review PDF Full Text: DOI
Iwano, Masahiro Applications of Nagumo-Hukuhara theory on the boundary value problems for nonlinear ordinary differential equations to Abrikosov problem and Falkner-Skan problem. (English) Zbl 0373.34006 Ann. Mat. Pura Appl., IV. Ser. 113, 303-392 (1977). MSC: 34B15 × Cite Format Result Cite Review PDF Full Text: DOI
Lukes, Jaroslav; Netuka, Ivan The Wiener type solution of the Dirichlet problem in potential theory. (English) Zbl 0319.31009 Math. Ann. 224, 173-178 (1976). MSC: 31C05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Elliott, Robert J.; Kalton, Nigel J. Cauchy problems for certain Isaacs-Bellman equations and games of survival. (English) Zbl 0302.90074 Trans. Am. Math. Soc. 198, 45-72 (1974). MSC: 91A23 91A05 31-XX × Cite Format Result Cite Review PDF Full Text: DOI
Hainer, Karl Lösung des Dirichletproblems und Konvergenz der Differenzenapproximation für elliptische Differentialgleichungen zweiter Ordnung. (German) Zbl 0253.35034 Math. Z. 131, 189-211 (1973). MSC: 35A35 65N12 65M99 65N99 35J25 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Schleinkofer, G. Das Cauchy-Problem bei quasilinearen parabolischen Differentialgleichungen mit unstetigen Anfangswerten. (German) Zbl 0211.13303 Math. Ann. 191, 337-346 (1971). MSC: 35K55 35K15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Schleinkofer, Gerhard Die erste Randwertaufgabe für quasilineare parabolische Differentialgleichungen bei unstetigen Randwerten. (German) Zbl 0189.41103 Math. Z. 113, 33-48 (1970). Reviewer: Kurt Hawlitschek (Ulm) MSC: 35K59 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Jackson, L. K. Subfunctions and second-order ordinary differential inequalities. (English) Zbl 0197.06401 Adv. Math. 2, 307-363 (1968). Reviewer: Lothar Berg (Rostock) MSC: 34Bxx × Cite Format Result Cite Review PDF Full Text: DOI
Loeb, Peter An axiomatic treatment of pairs of elliptic differential equations. (English) Zbl 0172.15101 Ann. Inst. Fourier 16, No. 2, 167-208 (1966). × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Nitsche, Johannes C. C. On new results in the theory of minimal surfaces. (English) Zbl 0135.21701 Bull. Am. Math. Soc. 71, 195-270 (1965). × Cite Format Result Cite Review PDF Full Text: DOI
Barrar, R. B. Some estimates for solutions of parabolic equations. (English) Zbl 0112.32502 J. Math. Anal. Appl. 3, 373-397 (1961). × Cite Format Result Cite Review PDF Full Text: DOI
Satō, Tokui Sur l’équation aux dérivées partielles \(\Delta z=f(x,y,z,p,q)\). II. (French) Zbl 0089.30803 Compos. Math. 14, 152-171 (1959). × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Brelot, M. Quelques développements récents sur le problème de Dirichlet. (French) Zbl 0088.07904 Abh. Math. Semin. Univ. Hamb. 23, 48-59 (1959). × Cite Format Result Cite Review PDF Full Text: DOI
Pernavs, Nora On a mixed boundary value problem of harmonic functions. (English) Zbl 0071.10102 Proc. Am. Math. Soc. 7, 127-130 (1956). × Cite Format Result Cite Review PDF Full Text: DOI
Stoll, Wilhelm Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlicher. I. II. (German) Zbl 0058.30705 Acta Math. 90, 1-115 (1953); 92, 55-169 (1954). × Cite Format Result Cite Review PDF Full Text: DOI
Brelot, Marcel La théorie moderne du potentiel. (French) Zbl 0055.08903 Ann. Inst. Fourier 4, 113-140 (1952). × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Royden, H. L. On the regularity of boundary points in potential theory. (English) Zbl 0046.10503 Proc. Am. Math. Soc. 3, 82-86 (1952). × Cite Format Result Cite Review PDF Full Text: DOI
Parreau, Michel Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann. (French) Zbl 0047.32004 Ann. Inst. Fourier 3, 103-197 (1951). × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Ohtsuka, Makoto Dirichlet problems on Riemann surfaces and conformal mappings. (English) Zbl 0043.30004 Nagoya Math. J. 3, 91-137 (1951). Reviewer: Leo Sario MSC: 30F35 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Brelot, Marcel Sur l’allure des fonctions harmoniques et sousharmoniques à la frontière. (French) Zbl 0042.10603 Math. Nachr. 4, 298-307 (1951). × Cite Format Result Cite Review PDF Full Text: DOI
Beckenbach, E. F. Convex functions. (English) Zbl 0041.38003 Bull. Am. Math. Soc. 54, 439-460 (1948). × Cite Format Result Cite Review PDF Full Text: DOI
Cimmino, Gianfranco Nuovo tipo di condizione al contorno e nuovo metodo die Nuovo tipo di condizione al contorno e nuovo metodo di trattazione per il problema generalizzato di Dirichlet. (Italian) Zbl 0019.26301 Rend. Circ. Mat. Palermo 61, 177-221 (1937). × Cite Format Result Cite Review PDF Full Text: DOI
Cimmino, G. Nuovo tipo di condizione al contorno e nuovo metodo di trattazione per il problema generalizzato di Dirichlet. (Italian) JFM 64.1163.01 Rend. Circ. mat. Palermo 61, 177-221 (1937). Reviewer: Perron, O., Prof. (München) × Cite Format Result Cite Review PDF Full Text: DOI
Petrowsky, I. Über das Irrfahrtproblem. (German) Zbl 0008.35603 Math. Ann. 109, 425-444 (1934). × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Petrowsky, I. Über das Irrfahrtsproblem. (German) JFM 60.1157.02 Math. Ann. 109, 425-444 (1934). Reviewer: Golomb, M., Dr. (Zagreb) × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Sternberg, W. Über die Gleichung der Wärmeleitung. (German) JFM 55.0290.14 Math. Ann. 101, 394-398 (1929). Reviewer: Haupt, Prof. O. (Erlangen) MSC: 35K05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML