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Nonlinear equations for fractional laplacians II: existence, uniqueness, and qualitative properties of solutions
dc.contributor.author | Cabré Vilagut, Xavier |
dc.contributor.author | Sire, Yannick |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2015-09-15T10:25:04Z |
dc.date.available | 2015-09-15T10:25:04Z |
dc.date.created | 2015-02-01 |
dc.date.issued | 2015-02-01 |
dc.identifier.citation | Cabre, X., Yannick, S. Nonlinear equations for fractional laplacians II: existence, uniqueness, and qualitative properties of solutions. A: "Transactions of the American Mathematical Society". 2015, p. 911-941. |
dc.identifier.issn | 0002-9947 |
dc.identifier.uri | http://hdl.handle.net/2117/76787 |
dc.description.abstract | This paper, which is the follow-up to part I, concerns the equation (-Delta)(s)v + G'(v) = 0 in R-n, with s is an element of (0, 1), where (-Delta)(s) stands for the fractional Laplacian-the infinitesimal generator of a Levy process.; When n = 1, we prove that there exists a layer solution of the equation (i.e., an increasing solution with limits +/- 1 at +/-infinity) if and only if the potential G has only two absolute minima in [-1, 1], located at +/- 1 and satisfying G'(-1) = G'(1) = 0. Under the additional hypotheses G ''(-1) > 0 and G ''(1) > 0, we also establish its uniqueness and asymptotic behavior at infinity. Furthermore, we provide with a concrete, almost explicit, example of layer solution.; For n >= 1, we prove some results related to the one-dimensional symmetry of certain solutions-in the spirit of a well-known conjecture of De Giorgi for the standard Laplacian. |
dc.format.extent | 31 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject.lcsh | Differential equations, Nonlinear |
dc.subject.other | elliptic-equations |
dc.subject.other | phase-transitions |
dc.subject.other | de-giorgi |
dc.subject.other | conjecture |
dc.subject.other | symmetry |
dc.subject.other | regularity |
dc.subject.other | space |
dc.title | Nonlinear equations for fractional laplacians II: existence, uniqueness, and qualitative properties of solutions |
dc.type | Part of book or chapter of book |
dc.subject.lemac | Equacions diferencials no lineals |
dc.contributor.group | Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
dc.identifier.doi | 10.1090/S0002-9947-2014-05906-0 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://www.ams.org/journals/tran/2015-367-02/S0002-9947-2014-05906-0/ |
dc.rights.access | Open Access |
local.identifier.drac | 15608846 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Cabre, X.; Yannick, S. |
local.citation.publicationName | Transactions of the American Mathematical Society |
local.citation.volume | 367 |
local.citation.number | 2 |
local.citation.startingPage | 911 |
local.citation.endingPage | 941 |
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