We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology
Iannizzotto, A., Mosconi, S., Squassina, M., H^s versus weighted-C^0 minimizers, <<NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS>>, 2015; 22 (3): 477-497. [doi:10.1007/s00030-014-0292-z] [http://hdl.handle.net/10807/87085]
H^s versus weighted-C^0 minimizers
Squassina, MarcoUltimo
2015
Abstract
We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology
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