Differentiability of solutions for a degenerate fully nonlinear free transmission problem
Edgard A. Pimentel, David Stolnicki
TL;DR
This paper proves that solutions to a complex nonlinear free transmission problem with degeneracy are differentiable, under minimal assumptions, advancing understanding of such mathematical models.
Contribution
It establishes the differentiability of viscosity solutions for a degenerate fully nonlinear free transmission problem under minimal degeneracy conditions.
Findings
Viscosity solutions are differentiable under minimal degeneracy assumptions.
The work extends regularity results to more general degenerate nonlinear problems.
Provides a foundation for further analysis of degenerate free transmission problems.
Abstract
We study a fully nonlinear free transmission problem in the presence of general degeneracy laws. Under minimal conditions on the degeneracy of the model, we establish the differentiability of viscosity solutions.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Nonlinear Differential Equations Analysis · Differential Equations and Boundary Problems