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oai:recercat.cat:2117/1190202026-02-04T07:42:48Zcom_2072_1033col_2072_452950

00925njm 22002777a 4500 dc Cabré Vilagut, Xavier author Lucia, Marcello author Sanchón, Manel author Villegas, Salvador author 2018-03-17 This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd rearrangement of an increasing function and we show that it decreases the energy functional when the weights satisfy a certain convexity-type hypothesis. This leads to the antisymmetry or oddness of increasing solutions (and not only of minimizers). We also prove a uniqueness result (which leads to antisymmetry) where a convexity-type condition by Berestycki and Nirenberg on the weights is improved to a monotonicity condition. In addition, we provide with a large class of problems where antisymmetry does not hold. Finally, some rather partial extensions in higher dimensions are also given. Peer Reviewed Postprint (author's final draft) Àrees temàtiques de la UPC::Matemàtiques i estadística Differential equations, Partial Antisymmetric solutions bistable nonlinearity continuous odd rearrangement monotonicity uniqueness weights Equacions diferencials parcials Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application Antisymmetry of solutions for some weighted elliptic problems