论文标题
$ p $ -laplacian对扰动的单拉式系统的薄弱解决方案是不断差异的
A weak solution to a perturbed one-Laplace system by $p$-Laplacian is continuously differentiable
论文作者
论文摘要
在本文中，我们旨在显示出弱解决方案对一个单板系统的连续可区分性，并以$ p $ -laplacian的扰动，$ 1 <p <\ p <\ infty $。该方程式的主要困难是，均匀的椭圆形在一个方面附近破裂，梯度消失的地方。我们想证明，即使在整个方面，弱解决方案的衍生物也是连续的。通过估计雅各布矩阵的Hölder连续性乘以其模量接近零的模量。为了显示此估计，我们考虑了一个近似系统，并使用标准方法，包括De Giorgi的截断和冻结系数参数。
In this paper we aim to show continuous differentiability of weak solutions to a one-Laplace system perturbed by $p$-Laplacian with $1<p<\infty$. The main difficulty on this equation is that uniform ellipticity breaks near a facet, the place where a gradient vanishes. We would like to prove that derivatives of weak solutions are continuous even across the facets. This is possible by estimating Hölder continuity of Jacobian matrices multiplied with its modulus truncated near zero. To show this estimate, we consider an approximated system, and use standard methods including De Giorgi's truncation and freezing coefficient arguments.
