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A priori estimates for semistable solutions of semilinear elliptic equations

Autor
Cabre, X.; Sanchon, M.; Spruck, J.
Tipus d'activitat
Article en revista
Revista
Discrete and continuous dynamical systems. Series A
Data de publicació
2016-02-01
Volum
36
Número
2
Pàgina inicial
601
Pàgina final
609
DOI
https://doi.org/10.3934/dcds.2016.36.601 Obrir en finestra nova
Projecte finançador
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repositori
http://arxiv.org/abs/1407.0243 Obrir en finestra nova
http://hdl.handle.net/2117/80798 Obrir en finestra nova
URL
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=11504 Obrir en finestra nova
Resum
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...
Citació
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.
Paraules clau
Semi-stable solutions, boundedness, dimension 4, extremal solutions, minimizers, regularity, semilinear elliptic equations
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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