Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems
Partial regularity of minimizers of functionals with discontinuous coefficients of low integrability with applications to nonlinear elliptic systems
复制标题
低可积不连续系数泛函极小值的部分正则性及其在非线性椭圆系统中的应用
DOI：
10.1080/03605302.2018.1517794
复制
发表时间：
2018
影响因子：
1.9
通讯作者：
C. Goodrich
中科院分区：
文献类型：
--
作者：
C. Goodrich
摘要在这篇文章中，我们考虑了开有界泛函的极小化问题。我们证明了即使系数a只满足这一点，仍然可以得出u在Da的正则点集上是部分Hölder连续的。我们注意到可积指数q > 1是任意的，因此系数映射可以是非常不规则的。作为应用，我们证明了椭圆型方程组的弱解满足同样的部分Hölder连续性.最后，我们还证明了Du几乎处处是Hölder连续的。
Abstract In this article, we consider minimizers of the functional where is open and bounded and . We show that even though the coefficient a satisfies only that , it nonetheless follows that u is partially Hölder continuous on the set of regular points of Da. We note that the integrability exponent q > 1 is arbitrary, and so, the coefficient map can be very irregular. As an application we show that weak solutions of the elliptic system satisfies the same partial Hölder continuity. The model case we have in mind is Finally, we also demonstrate that Du is also almost everywhere Hölder continuous.
具有 VMO 系数的二次函数极小值的偏正则性
DOI：
--
发表时间：
2005
期刊：
J. London Math. Soc.(2) 72
影响因子：
--
作者：
M. A. Ragusa;A. Tachikawa
通讯作者：
A. Tachikawa
DOI：
10.1090/s0002-9947-2012-05780-1
发表时间：
2011-08
期刊：
arXiv: Analysis of PDEs
影响因子：
--
作者：
M. Ragusa;A. Tachikawa;Hiroshi Takabayashi
通讯作者：
M. Ragusa;A. Tachikawa;Hiroshi Takabayashi