Minimizers of the \(W^{1, 1}\)-energy of \(\mathbb{S}^1\)-valued maps with prescribed singularities. Do they exist?

DOI10.1016/j.na.2018.04.013zbMath1408.46033OpenAlexW2801880245MaRDI QIDQ1626679

Petru Mironescu, Haim Brezis

Publication date: 21 November 2018

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2018.04.013

zbMATH Keywords

Sobolev spacesJacobiansingularitiescircle-valued maps

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Manifolds of mappings (58D15)

Cites Work

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• Harmonic maps with defects
• Functions with prescribed singularities
• Distances between classes in \(W^{1,1}(\Omega ;{\mathbb {S}}^{1})\)
• \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation
• The space \(\operatorname{BV}(S^2,S^1)\): minimal connection and optimal lifting
• The co-area formula for Sobolev mappings
• On the distributions of the form \(\sum_i(\delta_{p_i}-\delta_{n_i})\)

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