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.File in questo prodotto:
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