We prove an integral-representation result for limits of non-local quadratic forms on H-0(1)(Omega), with Omega a bounded open subset of R-d, extending the representation on C-c(infinity)(Omega) given by the Beurling Deny formula in the theory of Dirichletforms. We give a counter example showing that a corresponding representation may not hold if we consider analogous functionals in W-0(1,p)(Omega), with p not equal 2and 1 < p <= d
Validity and failure of the integral representation of Γ-limits of convex non-local functionals / Braides, A.; Dal Maso, G.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 286:6(2024). [10.1016/j.jfa.2024.110317]
Validity and failure of the integral representation of Γ-limits of convex non-local functionals
Braides A.;Dal Maso G.
2024-01-01
Abstract
We prove an integral-representation result for limits of non-local quadratic forms on H-0(1)(Omega), with Omega a bounded open subset of R-d, extending the representation on C-c(infinity)(Omega) given by the Beurling Deny formula in the theory of Dirichletforms. We give a counter example showing that a corresponding representation may not hold if we consider analogous functionals in W-0(1,p)(Omega), with p not equal 2and 1 < p <= d| File | Dimensione | Formato | |
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