Regularity results up to the boundary for minimizers of p(x)-energy with p(x)>1
Regularity results up to the boundary for minimizers of p(x)-energy with p(x)>1
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正则性结果达到 p(x)-能量最小值且 p(x)>1 的边界
DOI：
10.1007/s00229-016-0855-x
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发表时间：
2017
影响因子：
0.6
通讯作者：
Kunihiro Usuba
中科院分区：
文献类型：
--
作者：
Atsushi Tachikawa;Kunihiro Usuba
We show partial regularity up to the boundaryof a bounded open setfor minimizersuforp(x)-growth functionals of the following type $$\begin{aligned} {\mathcal A}(u)=\int _\varOmega \left( A^{\alpha \beta }_{ij}(x,u) D_{\alpha }u^i(x) D_{\beta }u^j(x)\right) ^{p(x)/2}dx, \end{aligned}$$assuming thatare bounded uniformly continuous functions satisfying Legendre condition and thatp(x) is a Hölder continuous function with. Whenare given as, we can also prove that minimizers have no singular points on the boundary.
We show partial regularity up to the boundaryof a bounded open setfor minimizersuforp(x)-growth functionals of the following type $$\begin{aligned} {\mathcal A}(u)=\int _\varOmega \left( A^{\alpha \beta }_{ij}(x,u) D_{\alpha }u^i(x) D_{\beta }u^j(x)\right) ^{p(x)/2}dx, \end{aligned}$$assuming thatare bounded uniformly continuous functions satisfying Legendre condition and thatp(x) is a Hölder continuous function with. Whenare given as, we can also prove that minimizers have no singular points on the boundary.