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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonlinear oblique boundary value problems for nonlinear elliptic equations

Authors: Gary M. Lieberman and Neil S. Trudinger
Journal: Trans. Amer. Math. Soc. 295 (1986), 509-546
MSC: Primary 35J65
MathSciNet review: 833695
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Abstract: We consider the nonlinear oblique derivative boundary value problem for quasilinear and fully nonlinear uniformly elliptic partial differential equations of second order. The elliptic operators satisfy natural structure conditions as introduced by Trudinger in the study of the Dirichlet problem while for the boundary operators we formulate general structure conditions which embrace previously considered special cases such as the capillarity condition. The resultant existence theorems include previous work such as that of Lieberman on quasilinear equations and Lions and Trudinger on Neumann boundary conditions.

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Article copyright: © Copyright 1986 American Mathematical Society