Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D

Abstract

We prove Lipschitz continuity of solutions to a class of rather general two-phase anisotropic free boundary problems in 2D and we classify global solutions. As a consequence, we obtain $C^{2,1}$ regularity of solutions to the Bellman equation in 2D.

References in corpus (1)

• Two-phase problems with distributed source: regularity of the free boundary

Cited by in corpus (4)

• Regularity Theory for Elliptic PDE
• An anisotropic monotoncity formula, with applications to some segregation problems
• An Elliptic Free Boundary Arising From the Jump of Conductivity
• Nodal Sets for Broken Quasilinear Partial Differential Equations with Dini Coefficients