Domain Variation Solutions for degenerate two phase free boundary problems
Aleksandr Dzhugan, Fausto Ferrari
TL;DR
This paper explores domain variation solutions and viscosity definitions for degenerate elliptic two-phase free boundary problems, addressing the challenges posed by degeneracy in the operator.
Contribution
It introduces a framework for understanding solutions to degenerate two-phase free boundary problems using domain variation and viscosity methods.
Findings
Developed a notion of domain variation solutions for degenerate problems
Established viscosity solution definitions for degenerate operators
Provided insights into the structure of free boundaries in degenerate contexts
Abstract
We discuss the domain variation solutions notion for some degenerate elliptic two-phase free boundary problems as well as the viscosity definition of the problem when the operator is degenerate.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Differential Equations Analysis