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

I. Birindelli; F. Demengel

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arXiv · 1002.2137

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

I. Birindelli·F. Demengel

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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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I. Birindelli, F. Demengel. 2010-02-10. One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations. https://arxiv.org/abs/1002.2137

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