Two-phase anisotropic free boundary problems and applications to the Bellman equation in 2D
Luis Caffarelli, Daniela De Silva, Ovidiu Savin
TL;DR
This paper establishes Lipschitz continuity and classifies global solutions for two-phase anisotropic free boundary problems in 2D, leading to $C^{2,1}$ regularity results for the Bellman equation in two dimensions.
Contribution
It introduces new regularity results for anisotropic free boundary problems and applies them to improve understanding of the Bellman equation in 2D.
Findings
Lipschitz continuity of solutions proven
Classification of global solutions achieved
$C^{2,1}$ regularity for Bellman equation in 2D obtained
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 regularity of solutions to the Bellman equation in 2D.
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