Computability of Harmonic Measure

Abstract: Abstract: We will review recent results relating the geometry of a connected domain to the computability of its harmonic measure at a given point x. In particular, we will discuss examples of domains whose harmonic measure at x is always computable relative to x, but not uniformly. This construction gives rise to examples of continuous functions arising as solutions to a Dirichlet problem (so they are even harmonic) which are piecewise computable (i.e. all their values are computable relative to the input point), but not computable.

analysis of PDEslogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic