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 p; q-growth conditions as in (1.2); in fact, we expect that Lavrentiev’s phenomenon does not occur if the quotient q=p is not too large in dependence of n, for instance, as in the cases – either scalar or vectorial ones – that we consider in this manuscript.
CalculusofVariations. – TheSobolevclasswhereaweaksolutionisalocalminimizer, by Filomena De Filippis, Francesco Leonetti, Paolo Marcellini and Elvira Mascolo, communicated on 10 February 2023
De Filippis F.;Leonetti F.;
2023-01-01
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 p; q-growth conditions as in (1.2); in fact, we expect that Lavrentiev’s phenomenon does not occur if the quotient q=p is not too large in dependence of n, for instance, as in the cases – either scalar or vectorial ones – that we consider in this manuscript.File in questo prodotto:
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