About the Geometry and Regularity of Largest Subsolutions for a Free Boundary Problem in R2: Elliptic Case
Betul Orcan
TL;DR
This paper investigates the geometric structure and regularity of the largest subsolutions in a one-phase free boundary problem in two dimensions, providing density bounds near the free boundary.
Contribution
It introduces new geometric and regularity results for the largest subsolutions under general free boundary conditions in R2.
Findings
Density bounds for positivity set near free boundary
Regularity properties of largest subsolutions
Geometric characterization of free boundary
Abstract
We study geometric and regularity properties of the largest subsolution of a one-phase free boundary problem under a very general free boundary condition in R2. Moreover, we provide density bounds for the positivity set and its complement near the free boundary.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Physics Problems · Differential Equations and Numerical Methods