TY - JOUR
AU - Savin, Ovidiu
AB - We investigate a fully nonlinear two-phase free boundary problem with a Neumann boundary condition on the boundary of a general convex set $K \subset \mathbb R^{n}$ with corners. We show that the interior regularity theory developed by Caffarelli for the classical two-phase problem in his pioneer works [3, 4] can be extended up to the boundary for the Neumann boundary condition under very mild regularity assumptions on the convex domain $K$. To start, we establish a general existence theorem for the Dirichlet two-phase problem driven by two different fully nonlinear operators, which is a result of independent interest.
TI - Two-Phase Problems: Perron Solutions and Regularity of the Neumann Problem in Convex Cones
JF - International Mathematics Research Notices
DO - 10.1093/imrn/rnaf152
DA - 2025-06-09
UR - https://www.deepdyve.com/lp/oxford-university-press/two-phase-problems-perron-solutions-and-regularity-of-the-neumann-S586Jkd3OK
VL - 2025
IS - 11
DP - DeepDyve
ER -