## Differential and Integral Equations

### Higher order Neumann problems for Laplace's equation in two dimensions

Michael Renardy

#### Abstract

We discuss the boundary value problem $\Delta u=f$, $\partial^ku/\partial n^k=g$ in a bounded two-dimensional domain. For a smooth simply connected region, we prove that the only solutions of the homogeneous problem are harmonic polynomials of degree $k-1$. For multiply connected domains, this is true generically." In domains with corners, on the other hand, there are additional solutions.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 10 (2002), 1273-1279.

Dates
First available in Project Euclid: 21 December 2012