Regularity of viscosity solutions to fully nonlinear elliptic transmission problems

M. Soria-Carro; P. R. Stinga

Regularity of viscosity solutions to fully nonlinear elliptic transmission problems

Analysis of PDEs 2023-10-09 v3

Authors: M. Soria-Carro , P. R. Stinga

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.

Keywords

regularity theory regularity for elliptic equations elliptic partial differential equations

Cite

@article{arxiv.2207.13772,
  title  = {Regularity of viscosity solutions to fully nonlinear elliptic transmission problems},
  author = {M. Soria-Carro and P. R. Stinga},
  journal= {arXiv preprint arXiv:2207.13772},
  year   = {2023}
}

Comments

38 pages. To appear in Advances in Mathematics

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