## Duke Mathematical Journal

### 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.

#### Article information

Source
Duke Math. J., Volume 115, Number 3 (2002), 479-512.

Dates
First available in Project Euclid: 26 May 2004

https://projecteuclid.org/euclid.dmj/1085598177

Digital Object Identifier
doi:10.1215/S0012-7094-02-11533-6

Mathematical Reviews number (MathSciNet)
MR1940410

Zentralblatt MATH identifier
1018.35024

#### Citation

Maz’ya, Vladimir. The Wiener test for higher order elliptic equations. Duke Math. J. 115 (2002), no. 3, 479--512. doi:10.1215/S0012-7094-02-11533-6. https://projecteuclid.org/euclid.dmj/1085598177