Searcharxiv⌕ Search

arXiv subjects

David Stolnicki

Publications and source records attributed to David Stolnicki.

4 recordsLinked to original sources
arXiv2025

Carleson-type removability for $p$-parabolic equations

We characterize removable sets for H\"older continuous solutions to degenerate parabolic equations of $p$-growth. A sufficient and necessary condition for a set to be removable is given in terms of an intrinsic parabolic Hausdorff measure, which depends on the considered H\"older exponent. We present a new method to prove the sufficient condition, which relies only on fundamental properties of the obstacle problem and supersolutions, and applies to a general class of operators. For the necessity of the condition, we establish the H\"older continuity of solutions with measure data, provided the measure satisfies a suitable decay property. The techniques developed in this article provide a new point of view even in the case $p=2$.

math.AP↗
arXiv2024

Boundary regularity for a fully nonlinear free transmission problem

We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the problem, we produce regularity estimates in Sobolev and $C^{1,{\rm Log-Lip}}$-spaces. Our findings extend recent developments in the literature to the free boundary setting.

math.AP↗
arXiv2021

On a class of fully nonlinear elliptic equation in dimension two

We study existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci's extremal operators in dimension two. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover for the $\mathcal{M}^-_{\lambda,\Lambda}$ operator, we show the existence of a critical exponent and give bounds for it.

math.AP↗