In this talk we illustrate the recent results established in a recent paper of the speaker on the existence, multiplicity and the asymptotic behavior of nontrivial solutions of nonlinear problems driven by the fractional Laplace operator and involving a critical Hardy potential. Some results are based on the fact that the main underlying elliptic functional is weakly lower semicontinuous and coercive. This property is proved as a direct consequence of the delicate study of the exact behavior of weakly convergent sequences in the space of measures. While for problems involving critical Sobolev terms this strategy does not work and the delicate point is the verification of the Palais--Smale condition at a special level. We overcome the difficulty using a tricky qualitative analysis, which we introduced successfully in the proof of a recent paper of the speaker.

Nonlocal Hardy-Sobolev critical elliptic Dirichlet problems

PUCCI, Patrizia
2015

Abstract

In this talk we illustrate the recent results established in a recent paper of the speaker on the existence, multiplicity and the asymptotic behavior of nontrivial solutions of nonlinear problems driven by the fractional Laplace operator and involving a critical Hardy potential. Some results are based on the fact that the main underlying elliptic functional is weakly lower semicontinuous and coercive. This property is proved as a direct consequence of the delicate study of the exact behavior of weakly convergent sequences in the space of measures. While for problems involving critical Sobolev terms this strategy does not work and the delicate point is the verification of the Palais--Smale condition at a special level. We overcome the difficulty using a tricky qualitative analysis, which we introduced successfully in the proof of a recent paper of the speaker.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1368054
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