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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A. Iannizzotto and S. Mosconi were supported by GNAMPA project: “Problemi al contorno per operatori non locali non lineari”. M. Squassina was supported by MIUR project: “Variational and topological methods in the study of nonlinear phenomena”. This work was partially carried out during a stay of S. Mosconi at the University of Verona. He would like to express his gratitude to the Department of Computer Science for the warm hospitality.
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Iannizzotto, A., Mosconi, S. & Squassina, M. H s versus C 0-weighted minimizers. Nonlinear Differ. Equ. Appl. 22, 477–497 (2015). https://doi.org/10.1007/s00030-014-0292-z
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DOI: https://doi.org/10.1007/s00030-014-0292-z