This article presents some qualitative results for solutions of the fully nonlinear elliptic equation F(∇u,D<sup>2</sup> u) + f(u) = 0 in R<sup>N</sup>. Precisely un- der some assumptions on f, if −1 &le u &le 1 and it converges to + and - 1 at infinity, uniformly with respect to x′, then the solution depends only on x<sub>1</sub>.
One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations / Birindelli, Isabella; F., Demengel. - STAMPA. - 528(2010), pp. 1-34. - CONTEMPORARY MATHEMATICS. [10.1090/conm/528/10410].
One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations
BIRINDELLI, Isabella;
2010
Abstract
This article presents some qualitative results for solutions of the fully nonlinear elliptic equation F(∇u,D2 u) + f(u) = 0 in RN. Precisely un- der some assumptions on f, if −1 &le u &le 1 and it converges to + and - 1 at infinity, uniformly with respect to x′, then the solution depends only on x1.File allegati a questo prodotto
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