We study compactness properties for solutions of a semilinear elliptic equation with critical nonlinearity. For high dimensions, we are able to show that any solutions sequence with uniformly bounded energy is uniformly bounded in the interior of the domain. In particular, singularly perturbed Neumann equations admit pointwise concentration phenomena only at the boundary.
Esposito, P. (2007). Interior estimates for some semilinear elliptic problem with critical nonlinearity. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 24(4), 629-644 [10.1016/j.anihpc.2006.04.004].
Interior estimates for some semilinear elliptic problem with critical nonlinearity
ESPOSITO, PIERPAOLO
2007-01-01
Abstract
We study compactness properties for solutions of a semilinear elliptic equation with critical nonlinearity. For high dimensions, we are able to show that any solutions sequence with uniformly bounded energy is uniformly bounded in the interior of the domain. In particular, singularly perturbed Neumann equations admit pointwise concentration phenomena only at the boundary.File in questo prodotto:
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