Displaying similar documents to “The first initial-boundary value problem for quasilinear second order parabolic equations”

Higher regularity for nonlinear oblique derivative problems in Lipschitz domains

Gary M. Lieberman (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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There is a long history of studying nonlinear boundary value problems for elliptic differential equations in a domain with sufficiently smooth boundary. In this paper, we show that the gradient of the solution of such a problem is continuous when a directional derivative is prescribed on the boundary of a Lipschitz domain for a large class of nonlinear equations under weak conditions on the data of the problem. The class of equations includes linear equations with fairly rough coefficients...

A survey of results on nonlinear Venttsel problems

Darya E. Apushkinskaya, Alexander I. Nazarov (2000)

Applications of Mathematics

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We review the recent results for boundary value problems with boundary conditions given by second-order integral-differential operators. Particular attention has been paid to nonlinear problems (without integral terms in the boundary conditions) for elliptic and parabolic equations. For these problems we formulate some statements concerning a priori estimates and the existence theorems in Sobolev and Hölder spaces.