(Non)local Γ-convergence

Serena Dipierro; Pietro Miraglio; Enrico Valdinoci

doi:10.6092/issn.2240-2829/10580

Authors

Serena Dipierro Department of Mathematics and Statistics, University of Western Australia,35 Stirling Highway, WA6009 Crawley http://orcid.org/0000-0003-4386-4485

Serena Dipierro took her PhD in Mathematical Analysis at the International School for Advanced Studies (SISSA, Trieste) in 2012. After PostDoc positions at the Universidad de Chile and University of Edinburgh, and a Humboldt Fellowship, she held permanent positions at the University of Melbourne and the Università di Milano. Since August 2018, she is Associate Professor at the University of Western Australia.
Pietro Miraglio Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milan; Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
Enrico Valdinoci Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, WA6009 Crawley http://orcid.org/0000-0001-6222-2272

Enrico Valdinoci received his PhD in Mathematics at the University of Texas at Austin in 2002 and later obtained a PostDoc Position at the Scuola Normale Superiore in Pisa. He was appointed Assistant/Associate Professor at the University of Rome Tor Vergata, Full Professor at the University of Milan, European Research Council Group Leader at the Weierstrass Institute in Berlin, and Professor at the University of Melbourne. Since August 2019, he is Professor at the University of Western Australia.

DOI:

https://doi.org/10.6092/issn.2240-2829/10580

Keywords:

Γ-convergence, pointwise convergence, energy and density estimates, long-range phase transitions, nonlocal perimeter, capillarity, water waves

Abstract

We present some long-range interaction models for phase coexistence which have recently appeared in the literature, recalling also their relation to classical interface and capillarity problems. In this note, the main focus will be on the Γ-convergence methods, emphasizing similarities and differences between the classical theory and the new trends of investigation. In doing so, we also obtain some new, more precise Γ-convergence results in terms of ``interior'' and ``exterior'' contributions. We also discuss the structural differences between Γ-limits and ``pointwise'' limits, especially concerning the ``boundary terms''.

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(Non)local Γ-convergence

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