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Interior estimates for some semilinear elliptic problem with critical nonlinearity. (English) Zbl 1151.35018

Summary: 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.

MSC:

35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J60 Nonlinear elliptic equations
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