Regularity of solutions to degenerate and singular free boundary problems with volume constraint
T. M. Nascimento, X. H. Nguyen, P. R. Stinga
TL;DR
This paper establishes the existence and regularity of solutions to complex free boundary problems involving degenerate and singular elliptic equations with a volume constraint on the positivity set.
Contribution
It introduces new methods to prove existence and regularity for free boundary problems with volume constraints in degenerate and singular elliptic cases.
Findings
Existence of solutions is proven.
Regularity of solutions is established.
Solutions satisfy the prescribed volume constraint.
Abstract
We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.
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