# Regularity of Lipschitz free boundaries for the thin one-phase problem

Daniela De Silva; Ovidiu Savin

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 6, page 1293-1326
- ISSN: 1435-9855

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topDe Silva, Daniela, and Savin, Ovidiu. "Regularity of Lipschitz free boundaries for the thin one-phase problem." Journal of the European Mathematical Society 017.6 (2015): 1293-1326. <http://eudml.org/doc/277693>.

@article{DeSilva2015,

abstract = {We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional $E(u,\Omega ) = \int _\Omega |\nabla u|^2 dX + \mathcal \{H\}^n(\lbrace u>0\rbrace \cap \lbrace x_\{n+1\} = 0\rbrace ), \quad \Omega \subset \mathbb \{R\}^\{n+1\},$ among all functions $u\ge 0$ which are fixed on $\partial \Omega $.},

author = {De Silva, Daniela, Savin, Ovidiu},

journal = {Journal of the European Mathematical Society},

keywords = {energy minimizers; one-phase free boundary problem; monotonicity formula; energy minimizers; one-phase free boundary problem; monotonicity formula},

language = {eng},

number = {6},

pages = {1293-1326},

publisher = {European Mathematical Society Publishing House},

title = {Regularity of Lipschitz free boundaries for the thin one-phase problem},

url = {http://eudml.org/doc/277693},

volume = {017},

year = {2015},

}

TY - JOUR

AU - De Silva, Daniela

AU - Savin, Ovidiu

TI - Regularity of Lipschitz free boundaries for the thin one-phase problem

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 6

SP - 1293

EP - 1326

AB - We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional $E(u,\Omega ) = \int _\Omega |\nabla u|^2 dX + \mathcal {H}^n(\lbrace u>0\rbrace \cap \lbrace x_{n+1} = 0\rbrace ), \quad \Omega \subset \mathbb {R}^{n+1},$ among all functions $u\ge 0$ which are fixed on $\partial \Omega $.

LA - eng

KW - energy minimizers; one-phase free boundary problem; monotonicity formula; energy minimizers; one-phase free boundary problem; monotonicity formula

UR - http://eudml.org/doc/277693

ER -

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