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

F. Demengel | Zendy; I. Birindelli | Zendy

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

Author(s) -

F. Demengel,

I. Birindelli

Publication year - 2010

Publication title -

contemporary mathematics - american mathematical society

Language(s) - English

Resource type - Reports

SCImago Journal Rank - 0.106

H-Index - 12

eISSN - 1098-3627

pISSN - 0271-4132

DOI - 10.1090/conm/528/10410

Subject(s) - mathematics , nonlinear system , bounded function , infinity , forcing (mathematics) , symmetry (geometry) , maxima and minima , type (biology) , term (time) , mathematical analysis , allen–cahn equation , variable (mathematics) , geometry , physics , quantum mechanics , ecology , biology

This article presents some qualitative results for solutions of the fully nonlinear elliptic equation F(∇u,D² u) + f(u) = 0 in R^N. 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

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