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 Università di Roma, Italy
boccardo@mat.uniroma1.it
[Abstract-pdf]
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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