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

Abstract

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We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional E ( u , Ω ) = ∫ Ω | ∇ u | 2 d X + ℋ n ( { u > 0 } ∩ { x n + 1 = 0 } ) , Ω ⊂ ℝ n + 1 , among all functions u ≥ 0 which are fixed on ∂ Ω .

How to cite

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De 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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