AI 中文总结
研究含哈密顿项的退化完全非线性自由传输问题，通过置于粘性不等式背景建立梯度局部赫尔德正则性，基于新估计与局部分析获逐点\(C^{1,\alpha}\)正则性。
AI 中文摘要
我们发展了含哈密顿项的退化完全非线性自由传输问题的粘性解正则性理论。通过将方程置于粘性不等式的背景下，建立了梯度的局部赫尔德正则性。此外，基于新的改进振荡型估计并结合局部分析，得到了精确的逐点\(C^{1,\alpha}\)正则性。
英文摘要
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 Hölder regularity of the gradient. In addition, based on a new improved oscillation-type estimate combined with a localized analysis, we obtain sharp pointwise $C^{1,α}$ regularity.
Comments36 pages. arXiv admin note: substantial text overlap with arXiv:2606.28949
