Harnack inequalities: an introduction.
Kassmann, Moritz (2007)
Boundary Value Problems [electronic only]
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Kassmann, Moritz (2007)
Boundary Value Problems [electronic only]
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Gary M. Lieberman (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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E. Di Benedetto (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
Neil S. Trudinger (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Bonforte, Matteo, Vazquez, Juan Luis (2007)
Boundary Value Problems [electronic only]
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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...