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

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

2010-02-10

arxiv.org/abs/1002.2137v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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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