论文标题
特定类别的单数抛物线方程的本地弱解决方案的新简短证明
A new short proof of regularity for local weak solutions for a certain class of singular parabolic equations
论文作者
论文摘要
我们将建立局部界限的弱解决方案的内部连续性，这些解决方案的原型为\ begin \ begin {equination} u_t = \ nabla \ cdot \ cdot \ big（| \ nabla u |^u |^{p-2} \ nabla u \ bigg） \ end {equation}和\ begin {equation} u_ {t} - \ nabla \ cdot（u^{m-1} | \ nabla u |^{p-2} {p-2} \ nabla u）= 0，\ quad \ text {for} \ quad} \ quad m+p> 3- \ 3- \ \ \ \ \ \ frac {p} {p} {p} {n} {n} {n} {n} { $ l^{1} $ - Harnack估计。
We shall establish the interior Hölder continuity for locally bounded weak solutions to a class of parabolic singular equations whose prototypes are \begin{equation} u_t= \nabla \cdot \bigg( |\nabla u|^{p-2} \nabla u \bigg), \quad \text{ for } \quad 1<p<2, \end{equation} and \begin{equation} u_{t}- \nabla \cdot ( u^{m-1} | \nabla u |^{p-2} \nabla u ) =0 , \quad \text{for} \quad m+p>3-\frac{p}{N}, \end{equation} via a new and simplified proof using recent techniques on expansion of positivity and $L^{1}$-Harnack estimates.
