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Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian

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10.3934/dcds.2010.28.1179
 
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hdl:2117/8303

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Cabré Vilagut, XavierMés informacióMés informacióMés informació
Cinti, Eleonora
Document typeArticle
Defense date2010-11
Rights accessRestricted access - publisher's policy
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
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.
CitationCabré, 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. 
URIhttp://hdl.handle.net/2117/8303
DOI10.3934/dcds.2010.28.1179
ISSN1078-0947
Publisher versionhttp://aimsciences.org/journals/pdfs.jsp?paperID=5131&mode=full
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