Free boundary regularity for a problem with right hand side

2009/12/10 by De Silva, Daniela · 8 citations
#35B65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0912.2057

Abstract

We consider a one-phase free boundary problem with variable coefficients and non-zero right hand side. We prove that flat free boundaries are C^1,α using a different approach than the classical supconvolution method of Caffarelli. We use this result to obtain that Lipschitz free boundaries are C^1,α.

Cited by

• Linearized equation and generic regularity in the Alt-Caffarelli problem
• Vectorial Bernoulli Problems and Free Boundary Systems
• Tangential touch between free and fixed boundaries for the fully nonlinear Alt-Phillips problem
• Non-minimizing Axially Symmetric Cavity Flow
• C^∞ Regularity for the free boundary of one-phase Fractional Laplacian problem
• Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle
• Fully nonlinear parabolic fixed transmission problems
• Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces

Related

• Free boundary regularity for a degenerate fully non-linear elliptic problem with right hand side
• Regularity of flat free boundaries for a p(x)-Laplacian problem with right hand side
• Free boundary regularity for fully nonlinear non-homogeneous two-phase problems
• C^2,α regularity of flat free boundaries for the thin one-phase problem
• Boundary Regularity for the Free Boundary in the One-phase Problem