2026-04-14T06:04:57Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/83032026-01-15T05:29:13Zcom_2072_1033col_2072_452950

Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian Cabré Vilagut, Xavier Cinti, Eleonora Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística Equacions diferencials parcials Classificació AMS::35 Partial differential equations We establish sharp energy estimates for some solutions, such as global minimizers, monotone solutions and saddle-shaped solutions, of the fractional nonlinear equation 1/2 in R n. Our energy estimates hold for every nonlinearity and are sharp since they are optimal for one-dimensional solutions, that is, for solutions depending only on one Euclidian variable. As a consequence, in dimension , we deduce the one-dimensional symmetry of every global minimizer and of every monotone solution. This result is the analog of a conjecture of De Giorgi on one-dimensional symmetry for the classical equation in R n. Peer Reviewed Postprint (published version) 2010-11 Article Cabré, X.; Cinti, E. Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian. "Discrete and continuous dynamical systems. Series A", Novembre 2010, vol. 28, núm. 3, p. 1179-1206. 1078-0947 https://hdl.handle.net/2117/8303 10.3934/dcds.2010.28.1179 eng http://aimsciences.org/journals/pdfs.jsp?paperID=5131&mode=full http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Restricted access - publisher's policy Attribution-NonCommercial-NoDerivs 3.0 Spain 28 p. application/pdf