Asymptotic behavior of the W1∕q,q-norm of mollified BV functions and applications to singular perturbation problems

DOI10.1051/cocv/2019051zbMath1471.46034arXiv1812.06358OpenAlexW2970230068MaRDI QIDQ5854369

Arkady Poliakovsky

Publication date: 17 March 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.06358

zbMATH Keywords

function of bounded variationfractional Sobolev normmollifiersingular perturbation functional

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Cites Work

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• Local and global minimizers for a variational energy involving a fractional norm
• \(\Gamma \)-convergence for nonlocal phase transitions
• A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
• Gamma-convergence of nonlocal perimeter functionals
• Upper bounds for singular perturbation problems involving gradient fields
• The effect of a singular perturbation on nonconvex variational problems
• On an open question about functions of bounded variation.
• Asymptotic expansions of the contact angle in nonlocal capillarity problems
• The gradient theory of phase transitions and the minimal interface criterion
• Line energies for gradient vector fields in the plane
• Regularity properties of nonlocal minimal surfaces via limiting arguments
• How to recognize convexity of a set from its marginals
• On lower semicontinuity of a defect energy obtained by a singular limit of the Ginzburg–Landau type energy for gradient fields
• Jump detection in Besov spaces via a new BBM formula. Applications to Aviles–Giga-type functionals