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arXiv · 2303.14520

Sharp regularity for a singular fully nonlinear parabolic free boundary problem

Damião J. Araújo·Ginaldo S. Sá·José Miguel Urbano
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Abstract

This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and the lack of a variational structure. The proof combines the power of the Ishii-Lions method with intrinsically parabolic oscillation estimates. The results are new, even for second-order linear operators in nondivergence form.

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Damião J. Araújo, Ginaldo S. Sá, José Miguel Urbano. 2023-03-25. Sharp regularity for a singular fully nonlinear parabolic free boundary problem. https://arxiv.org/abs/2303.14520

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