Γ-convergence for nonlocal phase transitions

By Ovidiu Savin, Enrico Valdinoci. 2012

204 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b545f6a0f876d1faf1af773fda520dd67fc2b42b

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Regularity properties of nonlocal minimal surfaces via limiting arguments (2011, background): “Besides their neat geometric motivation, such nonlocal minimal surfaces also arise as limit interfaces of nonlocal phase segregation problems, see [11,12].”
Nonlocal quantitative isoperimetric inequalities (2015, background): “The notion of fractional perimeter has been introduced in [36, 9] and it has been extensively studied in several recent papers (see for instance [24, 33, 34, 11, 18, 15] and references therein).”
Graph properties for nonlocal minimal surfaces (2015, background): “This nonlocal perimeter captures the global contributions between the set E and its complement and it is related to some models in geometry and physics, such as the motion by nonlocal mean curvature (see [8]) and the phase transitions in presence of long-range interactions (see [20]).”
Nonlocal Diffusion and Applications (2015, background): “For precise statements and further details, see [81].”
Local and global minimizers for a variational energy involving a fractional norm (2011, unknown): “Therefore, in the Appendix we collect some general and independent results involving the Gagliardo-type norm in (2), to be applied here and in [20,21,22], like construction of barriers, compactness results and various estimates, as well as regularity and limit properties for the solutions of equatio”
Sharp energy estimates for nonlinear fractional diffusion equations (2012, background): “the normal velocity is nonlocal of fractional-type. Later, Caﬀarelli, Roquejoﬀre, and Savin [8] set up the theory of nonlocal s-minimal surfaces for 0 < s < 1/2. Palatucci, Savin, and Valdinoci [22, 24, 25] have established precise relations between s-minimal surfaces and the interfaces of sem”