Regularity of viscosity solutions to fully nonlinear elliptic transmission problems

M. Soria-Carro; P. R. Stinga

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arXiv · 2207.13772

Regularity of viscosity solutions to fully nonlinear elliptic transmission problems

M. Soria-Carro·P. R. Stinga

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Abstract

We develop the regularity theory of viscosity solutions to transmission problems for fully nonlinear second order uniformly elliptic equations. Our results give a complete theory of existence, uniqueness, comparison principle, and regularity of solutions to flat interface transmission problems; and the $C^{0,\alpha}$, $C^{1,\alpha}$ and $C^{2,\alpha}$ regularity of viscosity solutions up to the transmission surface for the case of curved interfaces.

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M. Soria-Carro, P. R. Stinga. 2022-07-27. Regularity of viscosity solutions to fully nonlinear elliptic transmission problems. https://arxiv.org/abs/2207.13772

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