Continuity of some non-local functionals with respect to a convergence of the underlying measures

Andrea Braides; Gianni Dal Maso

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arXiv · 2204.01552

Continuity of some non-local functionals with respect to a convergence of the underlying measures

Andrea Braides·Gianni Dal Maso

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Abstract

We study some non-local functionals on the Sobolev space $W^{1,p}_0(\Omega)$ involving a double integral on $\Omega\times\Omega$ with respect to a measure $\mu$. We introduce a suitable notion of convergence of measures on product spaces which implies a stability property in the sense of $\Gamma$-convergence of the corresponding functionals.

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Andrea Braides, Gianni Dal Maso. 2022-04-04. Continuity of some non-local functionals with respect to a convergence of the underlying measures. https://arxiv.org/abs/2204.01552

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