Given an open and bounded set ω n and a family - = (X 1, ..., X m) of Lipschitz vector fields on ω, with m ≤ n, we characterize three classes of local functionals defined on first-order X-Sobolev spaces, which admit an integral representation in terms of X, i.e. F (u, A) = A f (x, u (x), X u (x)) x, with f being a Carathéodory integrand.
Integral representation of local functionals depending on vector fields / Essebei, F.; Pinamonti, A.; Verzellesi, S.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 2022:(2022), pp. 1-23. [10.1515/acv-2021-0054]
Integral representation of local functionals depending on vector fields
Essebei, F.;Pinamonti, A.;Verzellesi, S.
2022-01-01
Abstract
Given an open and bounded set ω n and a family - = (X 1, ..., X m) of Lipschitz vector fields on ω, with m ≤ n, we characterize three classes of local functionals defined on first-order X-Sobolev spaces, which admit an integral representation in terms of X, i.e. F (u, A) = A f (x, u (x), X u (x)) x, with f being a Carathéodory integrand.File in questo prodotto:
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