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.
H^s versus weighted-C^0 minimizers
IANNIZZOTTO, ANTONIO;MOSCONI, SUNRA JOHANNES NICOLAJ;SQUASSINA, Marco
2015-01-01
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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