Harmonic measure and heat equation
It is shown that the harmonic measure \(\omega_p\) of \(E\subseteq\partial \Omega\) at \(P\in\Omega\) for the (heat) operator \(\frac{\partial}{\partial t}- \frac{\partial^2} {\partial x^2}\) is absolutely continuous with respect to the length measure on \(\partial \Omega\) for \(C'{}^\alpha\) functions [see also \textit{R. P. Kaufman} and \textit{J. M. Wu}, J. Differ. Equations 80, 14-31 (1989; Zbl 0678.35042); ibid. 43, 204-234 (1982; Zbl 0534.31005)].
scientific article; zbMATH DE number 896436
scientific article