Abstract

We consider the problem min⁡v∈ CJ(v)\min\limits_{v\in\,C}J(v), where JJ is the standard integral functional J(v)=∫Ωj(x,∇v)−∫Ωf(x) v(x),J(v) = \int_{\Omega} j(x,{\nabla v}) - \int_{\Omega} f(x)\,v(x), defined in the Sobolev space W01,q(Ω)W_0^{1,q}(\Omega). We study the convergence of the minima uu if we perturb the convex set CC in accordance with the Mosco convergence.

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Keywords

  • Mosco convergence
  • minimization
  • integral functionals
  • continuous dependence
  • real analysis methods

Mathematics Subject Classification

49N99, 35J20, 35J60, 46T99

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Suggested citation

L. Boccardo. “Some New Results about Mosco Convergence.” Journal of Convex Analysis 28 (2021), No. 2, 387–394. https://doi.org/10.68381/jca28023

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Published by Heldermann Verlag, 2021. Rights now held by Banach Press LLC.