The Restriction Theorem for Fully Nonlinear Subequations

Details The Restriction Theorem for Fully Nonlinear Subequations The Restriction Theorem for Fully Nonlinear Subequations

2011-01-25

arxiv.org/abs/1101.4850v1

Mathematics

Analysis of PDEs

Scientific paper

Let X be a submanifold of a manifold Z. We address the question: When do viscosity sub-solutions of a fully nonlinear partial differential equation on Z, restrict to be viscosity sub-solutions of the restricted equation on X? It is not always true. In this paper we formulate a general result which guarantees good restriction. This is then applied to a long list of analytically and geometrically interesting cases.

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