Kodai Mathematical Journal

Convexity properties of Dirichlet integrals and Picone-type inequalities

Lorenzo Brasco and Giovanni Franzina

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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.

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Kodai Math. J., Volume 37, Number 3 (2014), 769-799.

First available in Project Euclid: 30 October 2014

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Brasco, Lorenzo; Franzina, Giovanni. Convexity properties of Dirichlet integrals and Picone-type inequalities. Kodai Math. J. 37 (2014), no. 3, 769--799. doi:10.2996/kmj/1414674621. https://projecteuclid.org/euclid.kmj/1414674621

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