A singular energy minimizing free boundary

Silva, Daniela De; Jerison, David

doi:10.1515/crelle.2009.074

Cited by 86 publications

(72 citation statements)

References 6 publications

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“…regularity away from possible singularities-similarly to what happens in minimal surface theory [15]. Recall that singularities may occur in the minimisation problem for the classical Laplacian case (see [12]). The following theorem is in the spirit of [1].…”

Section: Regularity Of the Free Boundarymentioning

confidence: 84%

Variational problems with free boundaries for the fractional Laplacian

Caffarelli¹,

Roquejoffre²,

Sire³

2010

J. Eur. Math. Soc.

245

234

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Abstract. We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.

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Section: Regularity Of the Free Boundarymentioning

confidence: 84%

Variational problems with free boundaries for the fractional Laplacian

Caffarelli¹,

Roquejoffre²,

Sire³

2010

J. Eur. Math. Soc.

245

234

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“…It is currently known that 4 ≤ k * ≤ 7. The lower bound follows from the work of Caffarelli, Jerison, and Kenig [6] and the upper bound has been proved by De Silva and Jerison [10].…”

Section: Catenoidal Alt-caffarelli Minimizersmentioning

confidence: 95%

Nonuniqueness in a Free Boundary Problem from Combustion

Petrosyan

Yip

2008

J Geom Anal

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We study a parabolic free boundary problem with a fixed gradient condition which serves as a simplified model for the propagation of premixed equidiffusional flames. We give a rigorous justification of an example due to J.L. Vázquez that the initial data in the form of two circular humps leads to the nonuniqueness of limit solutions if the supports of the humps touch at the time of their maximal expansion.

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“…The lower bound follows from [CJK04], and the upper bound was recently established by De Silva and Jerison [DSJ05]. The history of the problem is much shorter for 1 < p < ∞.…”

Section: Introductionmentioning

confidence: 90%