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Math. Anal."],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The present study concerns the nonlocal-to-local convergence of a family of exchange energy functionals in the limit of very short-range interactions. The analysis accounts for both symmetric and antisymmetric exchange. Our result is twofold. First, we extend the Bourgain\u2013Brezis\u2013Mironescu formula to encompass the scenario where antisymmetric contributions are encoded into the energy. Second, we prove that, under physically relevant assumptions on the families of exchange kernels, the family of nonlocal functionals gamma-converges to their local counterparts. As a by-product of our analysis, we obtain a rigorous justification of Dzyaloshinskii\u2013Moriya interactions in chiral magnets under the form commonly adopted in the variational theory of micromagnetism when modeling antisymmetric exchange interactions.<\/jats:p>","DOI":"10.1137\/24m1632577","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T04:29:58Z","timestamp":1730435398000},"page":"6995-7013","source":"Crossref","is-referenced-by-count":6,"title":["A Bourgain\u2013Brezis\u2013Mironescu Formula Accounting for Nonlocal Antisymmetric Exchange Interactions"],"prefix":"10.1137","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1715-5004","authenticated-orcid":true,"given":"Elisa","family":"Davoli","sequence":"first","affiliation":[{"name":"Institute of Analysis and Scientific Computing, TU Wien, 1040 Vienna, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0254-2957","authenticated-orcid":true,"given":"Giovanni","family":"Di Fratta","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Applicazioni \u201cR. Caccioppoli,\u201d Universit\u00e0 degli Studi di Napoli \u201cFederico II,\u201d 80126 Naples, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rossella","family":"Giorgio","sequence":"additional","affiliation":[{"name":"Institute of Analysis and Scientific Computing, TU Wien, 1040 Vienna, Austria, and MedUni Wien, 1090 Vienna, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,11,1]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-010-0399-4"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-8853(94)90046-9"},{"key":"ref3","first-page":"439","volume-title":"Optimal Control and Partial Differential Equations","author":"Bourgain J.","year":"2001"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-70914-7"},{"key":"ref5","first-page":"515","volume":"27","author":"Brezis H.","year":"2016","journal-title":"Atti Accad. Naz. 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