March 25, 2024Open Access

Brezis–Van Schaftingen–Yung formula in Orlicz spaces

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Abstract

In 14, Brezis–Van Schaftingen–Yung discovered new expression of the Sobolev semi-norm by replacing the Lp(R2N) norm in the Gagliardo Ws,p(RN) semi-norm with weak Lp(R2N) quasi-norm and setting s=1. In this paper we prove the same formula for functions in Orlicz–Sobolev spaces, in which the role of the power function t↦tp is performed by more general finite valued Young functions.

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Ioku et al. (Mon,) studied this question.

synapsesocial.com/papers/68e7275eb6db6435876a0ef3 https://doi.org/https://doi.org/10.1016/j.jmaa.2024.128350

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