T-minima on convex sets and Mosco-convergence

• Main Authors: Lucio Boccardo, Chiara Leone
• Format: Article
• Language: English
• Published: Sapienza Università Editrice 2020-06-01
• Series: Rendiconti di Matematica e delle Sue Applicazioni
• Subjects: mosco-convergence; t-minima; infinite energy minima.
• Online Access: https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2020(3-4)/223-236.pdf

Half century ago, Umberto Mosco was the ``relatore di tesi (tesi about the Mosco- convergence) di laurea'' of the first author; a quart of century ago, the first author was the ``relatore di tesi di laurea'' of the second author. The roots of this paper are the Mosco-convergence of convex sets and the minimization of integral functionals of the Calculus of Variations. We consider integral functionals of the type J(v)=∫Ω j(x,Dv)-∫Ω f(x)v(x). We study the existence of T-minima (infinite energy minima) on convex sets of the Sobolev space W01,p(Ω) and the stability of the T-minima under the Mosco-convergence of the convex sets.