학술논문

Continuity of some non-local functionals with respect to a convergence of the underlying measures
Document Type
Working Paper
Source
Subject
Mathematics - Analysis of PDEs
49J45, 46E35, 28A33, 28A35
Language
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.