The Wiener test for higher order elliptic equations

Abstract

We deal with strongly elliptic differential operators of an arbitrary even order $2m$ with constant real coefficients and introduce a notion of the regularity of a boundary point with respect to the Dirichlet problem which is equivalent to that given by N. Wiener in the case of $m=1$. It is shown that a capacitary Wiener's type criterion is necessary and sufficient for the regularity if $n=2m$. In the case of $n>2m$, the same result is obtained for a subclass of strongly elliptic operators.