积分微分自由传输问题的存在性与规律性

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-12 DOI:10.1112/blms.70070

Sun-Sig Byun, Seunghyun Kim

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引用次数: 0

摘要

研究了一类与解相关的bellman - isaacs型算子相关的积分-微分自由传输问题。通过构造合适的辅助问题的解，证明了该非局部问题的黏性解的存在性。我们还确定了在这种情况下，解的梯度具有内部Hölder规则性，其估计在方程的程度接近2时保持一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Existence and regularity for integro-differential free transmission problem

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Existence and regularity for integro-differential free transmission problem

We study an integro-differential free transmission problem associated with the Bellman–Isaacs-type operator that is solution-dependent. The existence of a viscosity solution is proved by constructing solutions of suitable auxiliary problems for such a nonlocal problem. We also identify circumstances under which the gradient of the solution enjoys an interior Hölder regularity whose estimates remain uniform as the degree of the equation approaches 2.

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