Abstract.
We prove the existence of classical solutions of elliptic equations of Monge-Ampère type subject to a semilinear oblique boundary condition which is a \(C^1\) perturbation of the Neumann boundary condition. Our techniques also allow us to treat fully nonlinear strictly oblique boundary conditions satisfying a concavity condition. Examples show that the above restrictions on the boundary condition are generally necessary for the existence of classical solutions.
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Received May 22, 1996 / Accepted April 10, 1997
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Urbas, J. Oblique boundary value problems for equations of Monge-Ampère type. Calc Var 7, 19–39 (1998). https://doi.org/10.1007/s005260050097
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DOI: https://doi.org/10.1007/s005260050097