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arXiv · 2210.15217

Absence of Lavrentiev's gap for anisotropic functionals

Michał Borowski·Iwona Chlebicka·Błażej Miasojedow
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Abstract

We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect to the last variable. This fact results from new results on good approximation properties of the natural underlying unconventional function space. Scalar and vector-valued problems are studied.

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Michał Borowski, Iwona Chlebicka, Błażej Miasojedow. 2022-10-27. Absence of Lavrentiev's gap for anisotropic functionals. https://arxiv.org/abs/2210.15217

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