Geodesic
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
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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.

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     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},
     year = {2002},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     mrnumber = {1994804},
     zbl = {1170.35423},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_111_0/}
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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/