Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/11373
DC Field | Value | Language |
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dc.contributor.author | Cabré, Xavier | - |
dc.contributor.author | Sanchón, Manel | - |
dc.date.accessioned | 2009-09-14T08:21:13Z | - |
dc.date.available | 2009-09-14T08:21:13Z | - |
dc.date.issued | 2006 | - |
dc.identifier.citation | Pré-Publicações DMUC. 06-07 (2006) | en_US |
dc.identifier.uri | https://hdl.handle.net/10316/11373 | - |
dc.description.abstract | We consider nonnegative solutions of −_pu = f(x, u), where p > 1 and _p is the p-Laplace operator, in a smooth bounded domain of RN with zero Dirichlet boundary conditions. We introduce the notion of semi-stability for a solution (perhaps unbounded). We prove that certain minimizers, or one-sided minimizers, of the energy are semi-stable, and study the properties of this class of solutions. Under some assumptions on f that make its growth comparable to um, we prove that every semi-stable solution is bounded if m < mcs. Here, mcs = mcs(N, p) is an explicit exponent which is optimal for the boundedness of semi-stable solutions. In particular, it is bigger than the critical Sobolev exponent p_ − 1. We also study a type of semi-stable solutions called extremal solutions, for which we establish optimal L1 estimates. Moreover, we characterize singular extremal solutions by their semi-stability property when the domain is a ball and 1 < p < 2 | en_US |
dc.description.sponsorship | MCYT, MEC Spanish grants BMF2002-04613-C03, MTM2005-07660-C02-01; CMUC/FCT | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Centro de Matemática da Universidade de Coimbra | en_US |
dc.rights | openAccess | en_US |
dc.title | Semi-stable and extremal solutions of reaction equations involving the p-laplacian | en_US |
dc.type | preprint | en_US |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
item.openairecristype | http://purl.org/coar/resource_type/c_816b | - |
item.openairetype | preprint | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Nacionais |
Files in This Item:
File | Description | Size | Format | |
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Semi-stable and extremal solutions of reaction equations.pdf | 217.53 kB | Adobe PDF | View/Open |
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