On parabolic convergence of positive solutions of the heat equation

热流的权不等式及Hardy-Hénon抛物方程的可解性

Two-weight inequality for the heat flow and solvability of Hardy-Hénon parabolic equation

本文通过稀疏控制方法给出了全空间上热流的权不等式，并利用该结果证明了具有Muckenhoupt类势的Hardy-Hénon抛物方程的局部和整体存在性。

热方程$L^p$ Dirichlet问题的可解性蕴含抛物一致可修正性

Solvability of the $L^p$ Dirichlet problem for the heat equation implies parabolic uniform rectifiability

本文证明在自然假设下，热方程Dirichlet问题的$L^p$可解性（等价于热测度满足弱-$A_\infty$条件）蕴含边界的抛物一致可修正性，确立了该几何性质作为抛物边界正则性的正确框架。

热方程$L^p$ Dirichlet问题的可解性等价于抛物型Lipschitz图情形下的抛物型一致可修正性

Solvability of the $L^p$ Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph

本文证明抛物型Lipschitz图域上热量测度的$A_\infty$性质等价于边界抛物型一致可修正性，从而结合Lewis-Murray工作解决了热方程$L^p$ Dirichlet问题可解性的长期开放问题。

On convergence of solutions to equilibria for quasilinear parabolic problems

We show convergence of solutions to equilibria for quasilinear parabolic evolution equations in situations where the set of equilibria is non-discrete, but forms a finite-dimensional $C^1$-manifold which is normally hyperbolic. Our results do not depend on the presence of an appropriate Lyapunov functional as in the Łojasiewicz-Simon approach, but are of local nature.