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Geometric inequalities for fractional Laplace operators and applications

  • Eleonora Cinti
  • Fausto FerrariEmail author
Article

Abstract

We prove a weighted fractional inequality involving the solution u of a nonlocal semilinear problem in \({\mathbb{R}^n}\) . Such inequality bounds a weighted L 2-norm of a compactly supported function ϕ by a weighted H s -norm of ϕ. In this inequality a geometric quantity related to the level sets of u will appear. As a consequence we derive some relations between the stability of u and the validity of fractional Hardy inequalities.

Keywords

Weighted Poincaré inequalities of fractional order Fractional Laplacian Hardy-type inequalities 

Mathematics Subject Classification

Primary 35J22 Secondary 35B65 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Wierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Dipartimento di Matematica dell’Università di BolognaBolognaItaly

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