Duke Mathematical Journal
- Duke Math. J.
- Volume 115, Number 3 (2002), 479-512.
The Wiener test for higher order elliptic equations
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.
Duke Math. J., Volume 115, Number 3 (2002), 479-512.
First available in Project Euclid: 26 May 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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