Volume 26, 2020
|Number of page(s)||20|
|Published online||02 October 2020|
Asymptotic behavior of the W1∕q,q-norm of mollified BV functions and applications to singular perturbation problems
Department of Mathematics, Ben Gurion University of the Negev,
PO Box 653,
* Corresponding author: firstname.lastname@example.org
Accepted: 25 August 2019
Motivated by results of Figalli and Jerison [J. Funct. Anal. 266 (2014) 1685–1701] and Hernández [Pure Appl. Funct. Anal., Preprint https://arxiv.org/abs/1709.08262 (2017)], we prove the following formula:
where Ω ⊂ ℝN is a regular domain, u ∈ BV (Ω) ∩ L∞(Ω), q > 1 and ηε(z) = ε−Nη(z∕ε) is a smooth mollifier. In addition, we apply the above formula to the study of certain singular perturbation problems.
Mathematics Subject Classification: 46E35
Key words: Function of bounded variations / mollifier, fractional Sobolev norm / singular perturbation functional
© EDP Sciences, SMAI 2020
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