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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 as well as Bellman equations.
@article{ASNSP_2002_5_1_1_111_0,
author = {Lieberman, Gary M.},
title = {Higher regularity for nonlinear oblique derivative problems in {Lipschitz} domains},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {111--151},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {1},
year = {2002},
mrnumber = {1994804},
zbl = {1170.35423},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_111_0/}
}
TY - JOUR AU - Lieberman, Gary M. TI - Higher regularity for nonlinear oblique derivative problems in Lipschitz domains JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 111 EP - 151 VL - 1 IS - 1 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_111_0/ LA - en ID - ASNSP_2002_5_1_1_111_0 ER -
%0 Journal Article %A Lieberman, Gary M. %T Higher regularity for nonlinear oblique derivative problems in Lipschitz domains %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 111-151 %V 1 %N 1 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_111_0/ %G en %F ASNSP_2002_5_1_1_111_0
Lieberman, Gary M. Higher regularity for nonlinear oblique derivative problems in Lipschitz domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 111-151. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_111_0/