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1 December 2002 The Wiener test for higher order elliptic equations
Vladimir Maz’ya
Duke Math. J. 115(3): 479-512 (1 December 2002). DOI: 10.1215/S0012-7094-02-11533-6

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.

Citation

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Vladimir Maz’ya. "The Wiener test for higher order elliptic equations." Duke Math. J. 115 (3) 479 - 512, 1 December 2002. https://doi.org/10.1215/S0012-7094-02-11533-6

Information

Published: 1 December 2002
First available in Project Euclid: 26 May 2004

zbMATH: 1018.35024
MathSciNet: MR1940410
Digital Object Identifier: 10.1215/S0012-7094-02-11533-6

Subjects:
Primary: 35J30
Secondary: 31B15 , 31B25

Rights: Copyright © 2002 Duke University Press

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Vol.115 • No. 3 • 1 December 2002
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