Boundary regularity for the free boundary in the one-phase problem
Héctor A. Chang‐Lara, Ovidiu Savin · Contemporary mathematics - American Mathematical Society · 2019
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.