Wiener-Type Criterion for Removability of the Heat Equation Fundamental Singularity
A geometric necessary-and-sufficient condition for when the fundamental singularity of the heat equation is removable — equivalently when the singular parabolic Dirichlet problem is uniquely solvable without prescribing the singular behavior. Removability is decided by the convergence of a series of parabolic h-capacities measuring the fine-topological thinness of the complementary set near the singularity, unifying measure-theoretic (parabolic measure) and probabilistic (conditional Brownian motion zero-one law) characterizations.
WIENER-TYPE CRITERION FOR THE REMOVABILITY OF THE FUNDAMENTAL SINGULARITY FOR THE HEAT EQUATION AND
This paper establishes a Wiener-type criterion characterizing when the fundamental singularity of the heat equation is removable, equivalently when the singular parabolic Dirichlet problem has a uniq…