对数双相问题的Hölder正则性
Hölder regularity for logarithmic double phase problems
浏览论文内容
中文总结 AI 辅助
研究一类具可变指数的广义对数双相方程弱解的有界性与正则性，通过一般结构假设在次临界情形下推导先验估计，利用多种技术证明全局Hölder连续性，扩展了相关正则性结果。
中文摘要 AI 辅助
我们研究了一类具有可变指数的广义对数双相方程弱解的有界性和正则性性质。所考虑的算子源于对数双相型的Musielak-Orlicz型能量，具有非标准增长特征。在一般结构假设下，我们在次临界情形下推导了先验有界性估计，并在存在临界增长项时建立了弱解的有界性。此外，我们通过De Giorgi迭代方案、局部化论证和冻结泛函技术证明了直至边界的全局Hölder连续性。所得结果扩展了双相及相关非标准增长问题的一些现有正则性结果。
英文摘要
We investigate boundedness and regularity properties of weak solutions to a class of generalized logarithmic double phase equations with variable exponents. The considered operators arise from Musielak-Orlicz type energies of logarithmic double phase type and exhibit nonstandard growth features. Under general structural assumptions, we derive a priori boundedness estimates in the subcritical setting and establish boundedness of weak solutions also in the presence of critical growth terms. In addition, we prove global Hölder continuity up to the boundary by means of the De Giorgi iteration scheme, localization arguments, and the frozen functional technique. The obtained results extend several existing regularity results for double phase and related nonstandard growth problems.
