2026-04-14T07:47:43Zhttps://recercat.cat/oai/request

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

Antisymmetry of solutions for some weighted elliptic problems Cabré Vilagut, Xavier Lucia, Marcello Sanchón, Manel Villegas, Salvador 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 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) 2018-03-17 Article https://www.tandfonline.com/doi/abs/10.1080/03605302.2018.1446168?journalCode=lpde20 http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain