Convexity properties of Dirichlet integrals and Picone-type inequalities

Lorenzo Brasco (1) , Giovanni Franzina (2)

1 I2M - Institut de Mathématiques de Marseille
2 Department Mathematik [Erlangen]

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 nonlinear positive eigenfunctions.

Mots clés: Nonlinear eigenvalue problems; maximum Principle; uniqueness of eigenfunctions; Hardy inequalities; nonlocal equations

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brasco, Giovanni Franzina. Convexity properties of Dirichlet integrals and Picone-type inequalities. Kodai Mathematical Journal, 2014, 37, pp.769-799. ⟨hal-00959091v2⟩