# Variational problems with free boundaries for the fractional Laplacian

Luis Caffarelli; Jean-Michel Roquejoffre; Yannick Sire

Journal of the European Mathematical Society (2010)

- Volume: 012, Issue: 5, page 1151-1179
- ISSN: 1435-9855

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topCaffarelli, Luis, Roquejoffre, Jean-Michel, and Sire, Yannick. "Variational problems with free boundaries for the fractional Laplacian." Journal of the European Mathematical Society 012.5 (2010): 1151-1179. <http://eudml.org/doc/277768>.

@article{Caffarelli2010,

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.},

author = {Caffarelli, Luis, Roquejoffre, Jean-Michel, Sire, Yannick},

journal = {Journal of the European Mathematical Society},

keywords = {fractional Laplacian; free boundary; fractional Laplacian; extension formula; free boundary problem; regularity; regularity of the free boundary; positive density},

language = {eng},

number = {5},

pages = {1151-1179},

publisher = {European Mathematical Society Publishing House},

title = {Variational problems with free boundaries for the fractional Laplacian},

url = {http://eudml.org/doc/277768},

volume = {012},

year = {2010},

}

TY - JOUR

AU - Caffarelli, Luis

AU - Roquejoffre, Jean-Michel

AU - Sire, Yannick

TI - Variational problems with free boundaries for the fractional Laplacian

JO - Journal of the European Mathematical Society

PY - 2010

PB - European Mathematical Society Publishing House

VL - 012

IS - 5

SP - 1151

EP - 1179

AB - 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.

LA - eng

KW - fractional Laplacian; free boundary; fractional Laplacian; extension formula; free boundary problem; regularity; regularity of the free boundary; positive density

UR - http://eudml.org/doc/277768

ER -

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