On J. Schauder's method to solve elliptic differential equations

DOI10.1007/s11784-011-0050-3zbMath1241.35090OpenAlexW2086507204MaRDI QIDQ644434

Manfred König

Publication date: 4 November 2011

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-011-0050-3

zbMATH Keywords

a priori estimatescontinuity methodregularity theoryLeray-Schauder principleexistence of \(C^{2,\alpha}\) solutions of linear and quasilinear elliptic equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) A priori estimates in context of PDEs (35B45) Quasilinear elliptic equations (35J62) Nonlinear boundary value problems for nonlinear elliptic equations (35J66) Classical solutions to PDEs (35A09)

Related Items (2)

Global \(C^1\) regularity of the value function in optimal stopping problems ⋮ S. Bernstein's idea for bounding the gradient of solutions to the quasi-linear Dirichlet problem

Cites Work

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• On Schauder's paper on linear elliptic differential equations
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• Potentialtheoretische Untersuchungen. I
• Über den funktionalen, insbesondere den analytischen Charakter der Lösungen elliptischer Differentialgleichungen zweiter Ordnung
• Über lineare elliptische Differentialgleichungen zweiter Ordnung
• Elliptic Partial Differential Equations of Second Order
• Über das Verhalten der Lösung des Dirichletproblems am Rand des Gebietes, wenn der Rand zur KlasseC^2αgehört
• On the Derivatives of Harmonic Functions on the Boundary
• Topologie et équations fonctionnelles

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