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Journal of Convex Analysis 28 (2021), No. 2, 387--394
Copyright Heldermann Verlag 2021

Some New Results about Mosco Convergence

Lucio Boccardo
Istituto Lombardo, Sapienza UniversitÓ di Roma, Italy


We consider the problem $\min\limits_{v\in\,C}J(v)$, where $J$ is the standard integral functional $$ J(v) = \int_{\Omega} j(x,{\nabla v}) - \int_{\Omega} f(x)\,v(x), $$ defined in the Sobolev space $W_0^{1,q}(\Omega)$. We study the convergence of the minima $u$ if we perturb the convex set $C$ in accordance with the Mosco convergence.

Keywords: Mosco convergence, minimization, integral functionals, continuous dependence, real analysis methods.

MSC: 49N99, 35J20, 35J60, 46T99.

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