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

Daniela De Silva; Ovidiu Savin

doi:10.4171/jems/531

JournalsjemsVol. 17, No. 6pp. 1293–1326

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

Daniela De Silva
Columbia University, New York, USA
Ovidiu Savin
Columbia University, New York, United States

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Abstract

We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional

E (u, Ω) = \int_{Ω} ∣\nabla u ∣^{2} d X + H^{n} ({u > 0} \cap {x_{n + 1} = 0}), Ω \subset R^{n + 1},

among all functions $u \geq 0$ which are fixed on $\partial Ω$ .

Cite this article

Daniela De Silva, Ovidiu Savin, Regularity of Lipschitz free boundaries for the thin one-phase problem. J. Eur. Math. Soc. 17 (2015), no. 6, pp. 1293–1326

DOI 10.4171/JEMS/531