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Título:	A priori estimates for semistable solutions of semilinear elliptic equations
Autor/a:	Cabré Vilagut, Xavier; Sanchón Rodellar, Manuel; Spruck, Joel
Otros autores:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
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 '.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Differential equations, Elliptic -Semi-stable solutions -extremal solutions -regularity -boundedness -semilinear elliptic equations -extremal solutions -dimension 4 -regularity -boundedness -minimizers -Equacions diferencials
Derechos:	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión publicada Artículo
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