Validity and failure of the integral representation of {\Gamma}-limits of convex non-local functionals
| Autor: | Braides, Andrea, Maso, Gianni Dal |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove an integral-representation result for limits of non-local quadratic forms on $H^1_0(\Omega)$, with $\Omega$ a bounded open subset of $\mathbb R^d$, extending the representation on $C^\infty_c(\Omega)$ 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 $W^{1,p}_0(\Omega)$, with $p\neq 2$ and $1 |
| Databáze: | arXiv |
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