We focus on three different convexity principles for local and nonlocal variational integrals. We prove various generalizations of them, as well as their equivalences. Some applications to nonlinear eigenvalue problems and Hardy-type inequalities are given. We also prove a measure-theoretic minimum principle for nonlocal and non- linear positive eigenfunctions. © 2014, Tokyo Institute of Technology. All rights reserved.

Convexity properties of Dirichlet integrals and Picone-type inequalities

Brasco, Lorenzo;FRANZINA, Giovanni
2014

Abstract

We focus on three different convexity principles for local and nonlocal variational integrals. We prove various generalizations of them, as well as their equivalences. Some applications to nonlinear eigenvalue problems and Hardy-type inequalities are given. We also prove a measure-theoretic minimum principle for nonlocal and non- linear positive eigenfunctions. © 2014, Tokyo Institute of Technology. All rights reserved.
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https://arxiv.org/abs/1403.0280
https://zbmath.org/?t=&s=0&q=Convexity+properties+of+Dirichlet+integrals+and+Picone-type+inequalities
Brasco, Lorenzo; Franzina, Giovanni
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/33110
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