Duke Mathematical Journal

The Wiener test for higher order elliptic equations

Vladimir Maz’ya

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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

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

First available in Project Euclid: 26 May 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30]
Secondary: 31B15: Potentials and capacities, extremal length 31B25: Boundary behavior


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

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