Full regularity of the free boundary in a bernoulli-type problem in two dimensions

Donatella Danielli; Arshak Petrosyan

doi:10.4310/MRL.2006.v13.n4.a14

Full regularity of the free boundary in a bernoulli-type problem in two dimensions

Donatella Danielli, Arshak Petrosyan

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0} ∩Ω in the Bernoulli-type problem governed by the p-Laplace operator J_p(u) = ∫_Ω (|∇u|^P + λ_p^p × {u>0}) dx → min, for p in the range 2 - ε₀ < p < ∞ for an absolute constant ε₀ > 0.

Original language	English (US)
Pages (from-to)	667-681
Number of pages	15
Journal	Mathematical Research Letters
Volume	13
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2006.v13.n4.a14
State	Published - Jul 2006
Externally published	Yes

Keywords

Bernoulli-type problem
Free boundary problem
Full regularity
p-Laplacian

ASJC Scopus subject areas

Mathematics(all)

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10.4310/MRL.2006.v13.n4.a14

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abstract = "In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0} ∩Ω in the Bernoulli-type problem governed by the p-Laplace operator Jp(u) = ∫Ω (|∇u|P + λpp × {u>0}) dx → min, for p in the range 2 - ε0 < p < ∞ for an absolute constant ε0 > 0.",

keywords = "Bernoulli-type problem, Free boundary problem, Full regularity, p-Laplacian",

author = "Donatella Danielli and Arshak Petrosyan",

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AU - Petrosyan, Arshak

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N2 - In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0} ∩Ω in the Bernoulli-type problem governed by the p-Laplace operator Jp(u) = ∫Ω (|∇u|P + λpp × {u>0}) dx → min, for p in the range 2 - ε0 < p < ∞ for an absolute constant ε0 > 0.

AB - In this note we prove that in dimension n = 2 there are no singular points on the free boundary ∂{u > 0} ∩Ω in the Bernoulli-type problem governed by the p-Laplace operator Jp(u) = ∫Ω (|∇u|P + λpp × {u>0}) dx → min, for p in the range 2 - ε0 < p < ∞ for an absolute constant ε0 > 0.

KW - Bernoulli-type problem

KW - Free boundary problem

KW - Full regularity

KW - p-Laplacian

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VL - 13

SP - 667

EP - 681

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 4

ER -

Full regularity of the free boundary in a bernoulli-type problem in two dimensions

Abstract

Keywords

ASJC Scopus subject areas

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