Convexity Properties of Dirichlet Integrals and Picone-type Inequalities
  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. 
Lorenzo Brasco and Giovanni Franzina
math.AP