The Sobolev class where a weak solution is a local minimizer
Filomena De Filippis
Università di L’Aquila, ItalyFrancesco Leonetti
Università di L'Aquila, ItalyPaolo Marcellini
Università di Firenze, ItalyElvira Mascolo
Università di Firenze, Italy
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Abstract
The aim of this paper is to propose some results which we hope could contribute to understand better Lavrentiev's phenomenon for energy integrals as in (1.1) under some -growth conditions as in (1.2); in fact, we expect that Lavrentiev's phenomenon does not occur if the quotient is not too large in dependence of , for instance, as in the cases – either scalar or vectorial ones – that we consider in this manuscript.
Cite this article
Filomena De Filippis, Francesco Leonetti, Paolo Marcellini, Elvira Mascolo, The Sobolev class where a weak solution is a local minimizer. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 34 (2023), no. 2, pp. 451–463
DOI 10.4171/RLM/1014