One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations

preprint2010arXivOpen access

Abstract

This article presents some qualitative results for entire solutions of the fully nonlinear elliptic equations of Allen Cahn type . Precisely under some additional assumptions on the forcing term, if the solution is bounded and converges uniformly at infinity in a fixed direction to its extrema, then the solution depends only on one variable.

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