The obstacle problem for a fractional Monge--Amp\`ere equation
Y. Jhaveri, P. R. Stinga
TL;DR
This paper investigates the obstacle problem for a nonlocal, degenerate elliptic Monge--Ampère equation, establishing existence, uniqueness, and regularity of solutions and their free boundaries.
Contribution
It introduces the first comprehensive analysis of the obstacle problem for a fractional Monge--Ampère equation, proving regularity results and free boundary properties.
Findings
Existence and uniqueness of classical solutions.
Regularity of solutions and free boundary.
Analysis of the free boundary structure.
Abstract
We study the obstacle problem for a nonlocal, degenerate elliptic Monge--Amp\`ere equation. We show existence and regularity of a unique classical solution to the problem and regularity of the free boundary.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Geometry and complex manifolds · Geometric Analysis and Curvature Flows