Fully nonlinear second order elliptic equations : recent development
Nicolai V. Krylov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Nicolai V. Krylov (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Cyril Imbert, Luis Silvestre (2016)
Journal of the European Mathematical Society
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We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.
Jensen, Robert R. (1998)
Documenta Mathematica
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L. Nirenberg (1988-1989)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Neil S. Trudinger (1973)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Amendola, M.E., Rossi, L., Vitolo, A. (2008)
Abstract and Applied Analysis
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Crandall, M.G., Kocan, M., Lions, P.L., Świȩch, A. (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Bardi, M., Bottacin, S. (1998)
Rendiconti del Seminario Matematico
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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...