Density of extremal measures in parabolic potential theory
The authors prove that, for the heat equation on \(\mathbb{R}^d\times \mathbb{R}\), any convex combination of harmonic measures \(\mu_{x}^{U_1} , \dots , \mu_{x}^{U_k}\), where \(U_1, \dots , U_k\) are relatively compact open neighborhoods of a given point \(x\), can be approximated by a sequence \(\mu_{x}^{W_n}\) of harmonic measures such that each \(W_n\) is an open neighborhood of \(x\) in \(U_1\cup \dots \cup U_k\). The corresponding result in the classical case was presented by the authors earlier in [Adv. Math. 218, No. 4, 1181--1223 (2008; Zbl 1146.31006)]. The authors give a new method of the proof.
scientific article; zbMATH DE number 5607252
scientific article