2019•Contemporary mathematics - American Mathematical SocietyOpen access

Boundary regularity for the free boundary in the one-phase problem

Héctor A. Chang‐Lara, Ovidiu Savin

Abstract

We consider the Bernoulli one-phase free boundary problem in a domain Ω \Omega and show that the free boundary F F is C 1 , 1 / 2 C^{1,1/2} regular in a neighborhood of the fixed boundary ∂ Ω \partial \Omega . We achieve this by relating the behavior of F F near ∂ Ω \partial \Omega to a Signorini-type obstacle problem.

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Key concepts: Free boundary problem, Boundary (topology), Obstacle problem, Omega, Mathematics, Domain (mathematical analysis), Bernoulli's principle, Obstacle