AI 中文总结
研究双相函数结构条件下的变分积分，通过De Giorgi型迭代论证建立非负局部拟极小值的强哈拿克不等式，为推导更一般变分泛函的哈拿克型不等式提供新视角，不依赖经典系数冻结策略。
AI 中文摘要
我们研究了一类在双相函数结构条件下的变分积分，该条件最近在文献[ADKO2026]中被引入。在此背景下，通过适当的De Giorgi型迭代论证，建立了非负局部拟极小值的强哈拿克不等式。最值得注意的是，本文提出的分析方法为在双相函数的Muckenhoupt型结构条件下，推导更一般变分泛函的哈拿克型不等式提供了新视角，且不依赖于基于调制系数的Hölder连续性和增长指数平衡条件的经典系数冻结策略。
英文摘要
We investigate a general class of variational integrals under a structural condition imposed on the double-phase function, recently introduced in~\cite{ADKO2026}. In this setting, the strong Harnack inequality for non-negative local quasi-minimizers is established via an appropriate De Giorgi-type iteration argument. Most notably, the proposed analytical approach in this paper provides a new perspective for deriving Harnack-type inequalities for more general variational functionals under a Muckenhoupt-type structural condition on the double-phase function, without relying on the classical coefficient-freezing strategy based on the Hölder continuity of the modulating coefficient and the balance condition on the growth exponents.
