Boundary regularity of minimizers of double phase functionals
Boundary regularity of minimizers of double phase functionals
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DOI：
10.1016/j.jmaa.2020.123946
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发表时间：
2020
影响因子：
1.3
通讯作者：
A. Tachikawa
中科院分区：
文献类型：
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作者：
A. Tachikawa
本文讨论了变指数双相泛函：|D u| g p（x）+ a（x）|D u|其中a（x）是非负α-Hölder连续函数，α∈（0，1），p（x）和q（x）是Hölder连续函数，1< p（x）≤ q（x）< p（x）+ α，| ξ|对于连续正定矩阵值函数g（x）=（g α β（x）），g：=（δ ijg α β（x）<$α i <$β j）1/2.我们证明了在适当的Dirichlet边界条件下，上述泛函的极小值在边界上是Hölder连续的。当g是Hölder连续时，我们还看到Du是局部Hölder连续的。
In this paper we treat the functional of double phase with variable exponents:∫(| D u| g p (x)+ a (x)| D u| g q (x)) d x, where a (x) is a non-negative α-Hölder continuous function with α∈(0, 1), p (x) and q (x) Hölder continuous functions with 1< p (x)≤ q (x)< p (x)+ α, and| ξ| g:=(δ i j g α β (x) ξ α i ξ β j) 1/2 for a continuous positive definite matrix valued function g (⋅)=(g α β (⋅)). We prove that the minimizer of the above functional with suitable Dirichlet boundary condition is Hölder continuous up to the boundary. When g is Hölder continuous, we see also that Du is locally Hölder continuous.