Uniform convergence of a singular perturbation problem

By Luis Caffarelli, A. Córdoba. 2010

129 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/eb8141bccafc000eaf77dca7f8de4b88d858bd77

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Interface Foliation near Minimal Submanifolds in Riemannian Manifolds with Positive Ricci Curvature (2010, background): “Indeed, analogous assertions hold true for general families of critical points, and for stronger notions of interface convergence, see [6, 29, 33].”
Regularity of flat level sets in phase transitions (2009, background): “In [8] Caffarelli and Cordoba proved a uniform density estimate for the level sets of local minimizers uε of Jε.”
On Phase-Separation Models: Asymptotics and Qualitative Properties (2013, background): “Thus the interface between the stable phases u = 1 and u = −1, represented by the sets [uε = λ] with |λ| < 1 approach a minimal hypersurface, see Caffarelli and Córdoba [11, 12], and also Röger and Tonegawa [41], for stronger convergence and uniform regularity results on these level surfaces.”
The Toda System and Clustering Interfaces in the Allen–Cahn equation (2008, background): “Other qualitative properties of minimizers can be found in [5,6,16,35,39].”
Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces. (2009, background): “For minimizers this convergence is known in very strong sense, see [3, 4].”
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, background): “well potential essentially modeled upon the functions (1.4) Fd(u) := |1− u2|d, with d > 0. In local settings, potentials of this kind were considered for instance by L. Caﬀarelli and A. Cordoba in [15, 16]. The strategy followed in [22, 23] for the construction of those minimizers relies on sever”
Stable solutions of the Allen–Cahn equation in dimension 8 and minimal cones (2011, methodology): “Gibbons’ Conjecture has been proved in all dimensions with different methods by Caffarelli and Córdoba [12], Farina [22], Barlow, Bass and Gui [6], and Berestycki, Hamel, and Monneau [7].”