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arXiv · 2304.04813

Asymptotic behavior of Musielak-Orlicz-Sobolev modulars

J. C. de Albuquerque·L. R. S. de Assis·M. L. M. Carvalho·A. Salort
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Abstract

In this article we study the asymptotic behavior of anisotropic nonlocal nonstandard growth seminorms and modulars as the fractional parameter goes to 1. This gives a so-called Bourgain-Brezis-Mironescu type formula for a very general family of functionals. In the particu\-lar case of fractional Sobolev spaces with variable exponent, we point out that our proof asks for a weaker regularity of the exponent than the considered in previous articles.

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J. C. de Albuquerque, L. R. S. de Assis, M. L. M. Carvalho, A. Salort. 2023-04-10. Asymptotic behavior of Musielak-Orlicz-Sobolev modulars. https://arxiv.org/abs/2304.04813

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