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.
2015
Fractional laplacian; Brezis-Nirenbergpe results
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/789774
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