On certain degenerate one-phase free boundary problems
Daniela De Silva, Ovidiu Savin
TL;DR
This paper develops a unified existence and regularity theory for a class of degenerate one-phase free boundary problems, encompassing classical problems like the obstacle problem and minimizers of the Alt-Phillips functional.
Contribution
It introduces a unified framework for analyzing degenerate one-phase free boundary problems, extending classical theories to more general settings.
Findings
Established existence and regularity results for the class of problems.
Unified treatment of classical free boundary problems and minimizers of the Alt-Phillips functional.
Provided new insights into the structure of solutions in degenerate cases.
Abstract
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more generally for minimizers of the Alt-Phillips functional.
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