Fractional Laplacian: Pohozaev identity and nonexistence results
Xavier Ros-Oton, Joaquim Serra
TL;DR
This paper derives a Pohozaev identity for the fractional Laplacian and uses it to prove the nonexistence of certain solutions in star-shaped domains with supercritical nonlinearities.
Contribution
It introduces a Pohozaev identity for the fractional Laplacian and applies it to establish nonexistence results for supercritical problems.
Findings
Pohozaev identity for fractional Laplacian derived
Nonexistence of nontrivial solutions in star-shaped domains
Results applicable to supercritical nonlinearities
Abstract
In this note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in star-shaped domains.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Differential Equations Analysis