Kodai Mathematical Journal

Convexity properties of Dirichlet integrals and Picone-type inequalities

Lorenzo Brasco and Giovanni Franzina

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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 nonlinear positive eigenfunctions.

Article information

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

Dates
First available in Project Euclid: 30 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1414674621

Digital Object Identifier
doi:10.2996/kmj/1414674621

Mathematical Reviews number (MathSciNet)
MR3273896

Zentralblatt MATH identifier
1315.47054

Citation

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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