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.

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/
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     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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