论文标题
具有强大类型潜力的可变系数抛物线运算符的强大独特延续
Strong unique continuation for variable coefficient parabolic operators with Hardy type potential
论文作者
论文摘要
在本文中，我们证明了以下缩放量表抛物线差异不平等的解决方案的强大独特的延续属性 \ [ | \ operatatorName {div}（a（x，t）\ nabla u） - u_t | \ leq \ frac {m} {| x |^{2}} | u |，\ \ \ \ \ \ \ \ \ \ \ \ \ \ \] 在$ x $和$ t $的情况下，系数矩阵$ a $是Lipschitz的连续。我们的主要结果使先前的船只与亚临界案例有关，并扩大了我们一个人的最新结果，即加洛法洛（Garofalo）和甘露（Manna）为热运算符。
In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality \[ |\operatorname{div} (A(x,t) \nabla u) - u_t| \leq \frac{M}{|x|^{2}} |u|,\ \ \ \ \] where the coefficient matrix $A$ is Lipschitz continuous in $x$ and $t$. Our main result sharpens a previous one of Vessella concerned with the subcritical case as well as extends a recent result of one of us with Garofalo and Manna for the heat operator.
