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(Quasi-)conformal methods in two-dimensional free boundary problems
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(Quasi-)conformal methods in two-dimensional free boundary problems
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Journal Article
(Quasi-)conformal methods in two-dimensional free boundary problems
2025
Overview
In this paper, we relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is locally a finite union of intervals and apply this result to the solutions of one-phase Bernoulli free boundary problems with geometric constraint. We also introduce a new conformal hodograph transform, which allows to obtain the precise expansion at branch points of both the solutions to the one-phase problem with geometric constraint and a class of symmetric solutions to the two-phase problem, as well as to construct examples of free boundaries with cusp-like singularities.
Publisher
European Mathematical Society (EMS)
Subject
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