The quasilinear dirichlet problem with decreased regularity at the boundary

DOI10.1080/03605308108820184zbMath0458.35039OpenAlexW2091119077MaRDI QIDQ3907910

Gary M. Lieberman

Publication date: 1981

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308108820184

zbMATH Keywords

Dirichlet problema priori estimatesquasilinear elliptic equationsexistence resultsdecreased regularity at the boundary

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65)

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Cites Work

• Unnamed Item
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• A general theory for linear elliptic partial differential equations
• Partial differential equations. 2nd ed
• Remarks relevant to minimal surfaces and to surfaces of prescribed mean curvature
• Über die Methode der a priori-Schranken
• Elliptic Partial Differential Equations of Second Order
• On harnack type inequalities and their application to quasilinear elliptic equations
• Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations.
• On Hölder continuity of solutions and their derivatives of linear and quasilinear elliptic and parabolic equations
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables
• Boundary regularity and embedded solutions for the oriented Plateau problem