Asymptotic behavior of Musielak-Orlicz-Sobolev modulars
Analysis of PDEs
2023-04-17 v2
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.
Keywords
Cite
@article{arxiv.2304.04813,
title = {Asymptotic behavior of Musielak-Orlicz-Sobolev modulars},
author = {J. C. de Albuquerque and L. R. S. de Assis and M. L. M. Carvalho and A. Salort},
journal= {arXiv preprint arXiv:2304.04813},
year = {2023}
}