A Note on Lipschitz Continuiy of the Solutions of a Class of Elliptic Free Boundary Problems
Abdeslem Lyaghfouri
TL;DR
This paper offers a straightforward proof using Harnack's inequality to establish Lipschitz continuity of solutions in a specific class of elliptic free boundary problems.
Contribution
It introduces a new, simplified proof technique for Lipschitz continuity in elliptic free boundary problems, enhancing theoretical understanding.
Findings
Lipschitz continuity of solutions proven using Harnack's inequality.
Simplified proof method compared to previous approaches.
Theoretical advancement in free boundary problem analysis.
Abstract
We provide a new and simple proof based on Harnack's inequality to the Lipschitz continuity of the solutions of a class of free boundary problems.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Differential Equations Analysis