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A priori estimates for semistable solutions of semilinear elliptic equations
dc.contributor.author | Cabré Vilagut, Xavier |
dc.contributor.author | Sanchón Rodellar, Manuel |
dc.contributor.author | Spruck, Joel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2015-12-16T11:34:13Z |
dc.date.available | 2015-12-16T11:34:13Z |
dc.date.issued | 2016-02-01 |
dc.identifier.citation | Cabre, X., Sanchon, M., Spruck, J. A priori estimates for semistable solutions of semilinear elliptic equations. "Discrete and continuous dynamical systems. Series A", 01 Febrer 2016, vol. 36, núm. 2, p. 601-609. |
dc.identifier.issn | 1078-0947 |
dc.identifier.uri | http://hdl.handle.net/2117/80798 |
dc.description.abstract | We consider positive semistable solutions u of Lu + f(u) = 0 with zero Dirichlet boundary condition, where L is a uniformly elliptic operator and f is an element of C-2 is a positive, nondecreasing, and convex nonlinearity which is super-linear at infinity. Under these assumptions, the boundedness of all semistable solutions is expected up to dimension n <= 9, but only established for n <= 4. In this paper we prove the L-infinity bound up to dimension n = 5 under the following further assumption on f: for every epsilon > 0, there exist T = T(epsilon) and C = C(epsilon) such that f '(t) < C f(t)(1+epsilon) for all t > T. This bound will follow from a L-p-estimate for f ' (u) for every p < 3 (and for all n >= 2). Under a similar but more restrictive assumption on f, we also prove the L-infinity estimate when n = 6. We remark that our results do not assume any lower bound on f '. |
dc.format.extent | 9 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Differential equations, Elliptic |
dc.subject.other | Semi-stable solutions |
dc.subject.other | extremal solutions |
dc.subject.other | regularity |
dc.subject.other | boundedness |
dc.subject.other | semilinear elliptic equations |
dc.subject.other | extremal solutions |
dc.subject.other | dimension 4 |
dc.subject.other | regularity |
dc.subject.other | boundedness |
dc.subject.other | minimizers |
dc.title | A priori estimates for semistable solutions of semilinear elliptic equations |
dc.type | Article |
dc.subject.lemac | Equacions diferencials |
dc.contributor.group | Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
dc.identifier.doi | 10.3934/dcds.2016.36.601 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11504 |
dc.rights.access | Open Access |
local.identifier.drac | 16978108 |
dc.description.version | Postprint (published version) |
dc.relation.projectid | info:eu-repo/grantAgreement/MINECO//MTM2014-52402-C3-1-P/ES/ECUACIONES EN DERIVADAS PARCIALES: PROBLEMAS DE REACCION-DIFUSION, INTEGRO-DIFERENCIALES Y GEOMETRICOS/ |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/FP7/320501/EU/Geometric analysis in the Euclidean space/ANGEOM |
local.citation.author | Cabre, X.; Sanchon, M.; Spruck, J. |
local.citation.publicationName | Discrete and continuous dynamical systems. Series A |
local.citation.volume | 36 |
local.citation.number | 2 |
local.citation.startingPage | 601 |
local.citation.endingPage | 609 |
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