Harmonic functions, defined as twice continuously differentiable functions satisfying Laplace’s equation, have long been a subject of intense study in both pure and applied mathematics. Their ...

We derive a mean value property for p-harmonic functions in two dimensions, 1 < p < ∞, which holds asymptotically in the viscosity sense. The formula coincides with the classical mean value property ...

The Annals of Probability, Vol. 15, No. 3 (Jul., 1987), pp. 954-984 (31 pages) We give conditions for transience and recurrence for certain diffusion processes in the plane which "look" recurrent in ...

THE object of this work is to provide a text-book on the elements of the theory of spherical harmonics with applications to mathematical physics so far as this can be done without employing contour ...