A Geometric Approach to Free Boundary Problems

By Luis Caffarelli, Sandro Salsa. 2005

484 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/78f2dad1747e8a9aed875b8982916b4e64df1d90

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In Applied Mathematics

Citations in the corpus

Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian (2007, background): “The proof follows by a standard argument in the subject [4], [6].”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, methodology): “, but the methods were dierent. 2Nash and Nirenberg shared the Abel Prize for 2015. 16 The Obstacle Problem. This is the most famous free boundary problem and there is a huge literature for it, cf. [64, 67, 127, 169] and their references. It belongs to the class of stationary problems, connected wit”
Minimization of the k-th eigenvalue of the Dirichlet Laplacian (2012, background): “In the literature, the regularity of the free boundaries is well understood only for energy like minimizers (see [1,2,8,11]).”
Regularity Theory for Elliptic PDE (2022, result): “We will not prove such theorem here; we refer to [DS19] for a short proof of the result (see also [CS05]), as well as to [AS19] for a more general version that allows equations with a right hand side.”
Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames (2007, methodology): “Also, recall that Y0 and YF are uniformly α-Holder for some α> 0. This implies that up to a change of coordinates, we are in the conditions of application of Lemma 2.1 of [ 9 ].”
On some Free Boundary Problems of the Prey-predator Model (2013, background): “There is a vast literature on the Stefan problems, and some important theoretical advances can be found in [2, 5] and the references therein.”
Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case (2014, background): “≤ γ ( xn + εn + Ck −1/4 n ) + γ ( yn + εn + Ck −1/4 n ) ≤ γ(xn) + γ(yn) + Cεn + Ck−1/4 n , where the first inequality is a consequence of the fact that fn and gn have disjoint support (this is nothing but the well-known optimal partition problem of the sphere which serves as keystone in the proof of”
Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary (2010, unknown): “There is a vast literature on the Stefan problem, and some important recent theoretical advances can be found in [5].”
Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆ (2011, background): “There is a vast literature on the Stefan problem, and some important recent theoretical advances can be found in [5].”
Free Boundary Problems for a Lotka–Volterra Competition System (2014, background): “There is a vast literature on the Stefan problems, and some important theoretical advances can be found in [2, 5] and the references therein.”
Global $C^{1}$ regularity of the value function in optimal stopping problems (2018, unknown): “167, for a definite result of this kind dating back to Gevrey [22] as well as [4] and [5], Chapter 8, for related results in higher dimensions).”