Gradient regularity for degenerate fully nonlinear free transmission problems with Hamiltonian terms

Wentao Huo

Gradient regularity for degenerate fully nonlinear free transmission problems with Hamiltonian terms

Analysis of PDEs 2026-07-09 v1

Authors: Wentao Huo

Abstract

We develop the regularity theory of viscosity solutions to degenerate fully nonlinear free transmission problems with Hamiltonian terms. By framing the equation in the context of viscosity inequalities, we establish local H\"{o}lder regularity of the gradient. In addition, based on a new improved oscillation-type estimate combined with a localized analysis, we obtain sharp pointwise $C^{1,\alpha}$ regularity.

Keywords

degenerate fully nonlinear free transmission problems Hamiltonian terms viscosity solutions gradient regularity Hölder regularity

Cite

@article{arxiv.2607.08919,
  title  = {Gradient regularity for degenerate fully nonlinear free transmission problems with Hamiltonian terms},
  author = {Wentao Huo},
  journal= {arXiv preprint arXiv:2607.08919},
  year   = {2026}
}

Comments

36 pages. arXiv admin note: substantial text overlap with arXiv:2606.28949