Some new monotonicity theorems with applications to free boundary problems

By Luis Caffarelli, David Jerison, Carlos E. Kenig. 2002

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a2890c2e77687c0e032cb0196a1ab21010865bb4

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Two-phase problems with distributed sources: regularity of the free boundary (2012, background): “5 in [Caffarelli et al. 2002], to recover the Lipschitz continuity of a viscosity solution.”
A variational problem for the spatial segregation of reaction-diffusion systems (2003, methodology): “In this paper we shall take advantage of the following formula which is proven in [6].”
Asymptotic estimates for the spatial segregation of competitive systems (2005, methodology): “In order to establish our Liouville results, we need to provide suitable monotonicity-type formula, on the line of [1, 5 ], which applies to the solutions of (1) and to the element of S, for any k and in any dimension.”
Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case (2014, methodology): “Since we will make use of several monotonicity formulae, this would be very technical and not always easy; the reader can easily understand what we mean by looking at the contribution [16], where the classical Caffarelli-Jerison-Kenig monotonicity formula has been extended to systems with variable c”
An optimal partition problem related to nonlinear eigenvalues (2003, background): “The fact that ' is finite is shown in the proof of Lemma 2.1 of [ 4 ].”
Lipschitz continuity of state functions in some optimal shaping (2005, methodology): “here, we apply the ad hoc “monotonicity Lemma” of [3] in its non homogeneous version given in [ 6 ].”
Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion Flames (2007, methodology): “is nonincreasing. Arguing as in Step 1 of Theorem 5.1 of [ 8 ] implies the boundedness of e −1/3 (YO,F − Ae 1/3 ). Hence the result can be reached in a straightforward way.”