变指数双相泛函极小元的正则性
Regularity for Minimizers for Double Phase Functionals with Variable Exponents
DOI: 10.12677/AAM.2026.153100, PDF,   
作者: 周梓宸：浙江师范大学数学科学学院，浙江 金华
关键词: 双相泛函；极小元；正则性；增长条件；Double Phase Functionals； Minimizers； Regularity； Growth Conditions
摘要: 本文研究了一类具有变指数的双相变分泛函极小元的正则性问题. 这类泛函由两个具有不同增长指 数的项组成，相较于传统研究中指数为常数的情形，变指数情形下的双相泛函具有更强的非一致 椭圆性和非标准增长特征, 另外变指数的引入使得模型更好地适应非均匀介质。
Abstract: This paper investigates the regularity properties of minimizers for a class of double phase variational functionals with variable exponents. The functional under consider-ation consists of two terms with distinct growth exponents. Compared to the classical setting with constant exponents, the variable exponent case exhibits stronger non u- niform ellipticity and nonstandard growth characteristics, and the variable exponents enables the model to better adapt to non-uniform media.
文章引用：周梓宸. 变指数双相泛函极小元的正则性[J]. 应用数学进展, 2026, 15(3): 213-224. https://doi.org/10.12677/AAM.2026.153100

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