论文标题
加权Sobolev空间的扩散半群的规律性估计
Regularity estimates for diffusion semigroups on weighted Sobolev spaces
论文作者
论文摘要
在这项工作中，我们考虑了具有光滑和有限系数的一类二阶均匀的椭圆运算符。我们提供了有关这些操作员在加权Sobolev空间上产生的半群的规范的估计，其中重量满足某些特定的条件。我们的证明依赖于对抛物线方程基本解决方案的衍生物的经典界限。
In this work, we consider a class of second order uniformly elliptic operators with smooth and bounded coefficients. We provide some estimates on the norm of the semigroup generated by these operators acting on weighted Sobolev spaces, where the weight satisfies some specific conditions. Our proof relies on a classical bound for the derivatives of fundamental solution to parabolic equations.
