$C^{\infty}$ regularity of certain thin free boundaries
Daniela De Silva, Ovidiu Savin
TL;DR
This paper proves that certain smooth free boundaries in the thin one-phase problem are actually infinitely differentiable, advancing understanding of boundary regularity in free boundary problems.
Contribution
It establishes that $C^{2,eta}$ free boundaries in the thin one-phase problem are smooth, extending previous regularity results.
Findings
$C^{2,eta}$ free boundaries are smooth
Regularity results extend to higher smoothness levels
Advances understanding of free boundary regularity
Abstract
We continue our study of the free boundary regularity in the thin one-phase problem and show that free boundaries are smooth.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows