Asymptotic behavior of the W 1/q,q -norm of mollified BV functions and applications to singular perturbation problems

Arkady Poliakovsky

doi:10.1051/cocv/2019051

Asymptotic behavior of the W ^1/q,q-norm of mollified BV functions and applications to singular perturbation problems

Arkady Poliakovsky

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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: [formula presented] is a smooth mollifier. In addition, we apply the above formula to the study of certain singular perturbation problems.

Original language	English
Article number	2019051
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	26
DOIs	https://doi.org/10.1051/cocv/2019051
State	Published - 1 Jan 2020

Keywords

Function of bounded variations
Mollifier, fractional Sobolev norm
Singular perturbation functional

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Computational Mathematics

Access to Document

10.1051/cocv/2019051

Cite this

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abstract = "Motivated by results of Figalli and Jerison [J. Funct. Anal. 266 (2014) 1685-1701] and Hern{\'a}ndez [Pure Appl. Funct. Anal., Preprint https://arxiv.org/abs/1709.08262 (2017)], we prove the following formula: [formula presented] is a smooth mollifier. In addition, we apply the above formula to the study of certain singular perturbation problems.",

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KW - Function of bounded variations

KW - Mollifier, fractional Sobolev norm

KW - Singular perturbation functional

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