Validity and failure of the integral representation of Γ-limits of convex non-local functionals
Loading...
Date
2023-05-09
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We prove an integral-representation result for limits of non-local quadratic forms on H1
0 pΩq, with Ω a bounded open subset of Rd, extending the representation on C8c
pΩq given by the Beurling-Deny formula in the theory of Dirichlet forms. We give
a counterexample showing that a corresponding representation may not hold if we
consider analogous functionals in W1,p0 pΩq, with p ‰ 2 and 1 ă p ď d.
Description
Preprint number SISSA/06/2023
Keywords
Γ-convergence, Dirichlet forms, non-local functionals, integral representation