论文标题
具有非标准生长和不连续系数的退化抛物线系统的部分规律性
Partial regularity for degenerate parabolic systems with non-standard growth and discontinuous coefficients
论文作者
论文摘要
本文研究了某些退化抛物线系统的弱解决方案的部分Hölder连续性，其模型是可区分的抛物线$ p（x，t）$ - laplacian系统，\ begin \ begin {equation*} \ partial_t u- \ operatorAname {div} [μ（z）（1+ | du |^2）^{\ frac {\ frac {p（z）-2} {2}} {2}} du] = 0，\ qquad p（z）\ geq2。我们表明，如果$μ（z）$满足一定的VMO型条件，则$ u $是本地hölder连续的，除了零度零集。
This article studies the partial Hölder continuity of weak solutions to certain degenerate parabolic systems whose model is the differentiable parabolic $p(x,t)$-Laplacian system, \begin{equation*}\partial_t u-\operatorname{div}[μ(z)(1+|Du|^2)^{\frac{p(z)-2}{2}}Du]=0,\qquad p(z)\geq2.\end{equation*} Here, the exponential function $p(z)$ satisfies a logarithmic continuity condition. We show that if $μ(z)$ satisfies a certain VMO-type condition, then $u$ is locally Hölder continuous except for a measure zero set.
