Convexity properties of Dirichlet integrals and Picone-type inequalities
By Lorenzo Brasco, Giovanni Franzina. 2014
172 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/63c3bae7a1208000f56a9db74efad43ac395e925
How researchers see this paper
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In Applied Mathematics
- Marco Squassina
- Kanishka Perera
- Shibo Liu
- Lorenzo Brasco
- Antonio Iannizzotto
- Alexander Quaas
- L. D. Pezzo
- Ariel Martin Salort
In Mathematical Physics
- Marco Squassina
- Lorenzo Brasco
- Kanishka Perera
- Shibo Liu
- Enea Parini
- Antonio Iannizzotto
- Ariel Martin Salort
- Alexander Quaas
Citations in the corpus
- Eigenvalues and minimizers for a non-standard growth non-local operator (2018, background): “This line of research was widely continued, only to mention a few works, we remit to [6, 7, 15] and references to these papers.”
- A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian (2016, background): “To this end, we follow the ideas in [4] and prove first the next logarithmic lemma (see [12, Lemma 1.”
- Existence results for fractional p-Laplacian problems via Morse theory (2014, result): “More recently Di Castro, Kuusi and Palatucci [13] and Brasco and Franzina [3] obtained relevant results about the local boundedness and Hölder continuity for the solutions to the problem of finding (s, p)-harmonic functions u, that is (−Δ)pu = 0 inΩwith u = g onR N \ Ω, for some function g, providin”
- Nonlocal problems with critical Hardy nonlinearity (2017, unknown): “A Picone identity in the fractional setting has been obtained in [2] and reads as [v]s,p ≥ 〈(−∆p) u, vp (u+ ε)p−1 〉, ∀ε > 0, u, v ≥ 0.”
- The second eigenvalue of the fractional p-Laplacian (2014, background): “4], which is based on the so-called hidden convexity for Dirichlet integrals (see [3]).”