Regularity for minimizers for functionals of double phase with variable exponents
Regularity for minimizers for functionals of double phase with variable exponents
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DOI：
10.1515/anona-2020-0022
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发表时间：
2019-07
影响因子：
4.2
通讯作者：
M. Ragusa;A. Tachikawa
中科院分区：
文献类型：
--
作者：
M. Ragusa;A. Tachikawa
双相型H（u）：= ∞的泛函|杜|p+a（x）|杜|qdx，（q>p>1，a（x）≥0）$$\开始{array}{} \displaystyle {\cal H}（u）：= \int \left（|杜|^{p} + a（x）|杜|^{q} \right）dx，~（q \gt p \gt 1，~~a（x）\geq 0）\end{array}$$在Colombo-Mingione [1]对常数p和q的划时代的论文中被引入，并由他们和Baroni研究。他们获得了尖锐的规律性结果极小的功能。本文讨论了指数是x的函数的情况，并部分推广了它们的正则性结果。
Abstract The functionals of double phase type H(u):=∫|Du|p+a(x)|Du|qdx, (q>p>1, a(x)≥0) $$\begin{array}{} \displaystyle {\cal H} (u):= \int \left(|Du|^{p} + a(x)|Du|^{q} \right) dx, ~~ ~~~(q \gt p \gt 1,~~a(x)\geq 0) \end{array}$$ are introduced in the epoch-making paper by Colombo-Mingione [1] for constants p and q, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of x and partly generalize their regularity results.