The Wiener test for higher order elliptic equations

Maz’ya, Vladimir

Duke Math. J., Tome 115 (2002) no. 1, p. 479-512 / Harvested from Project Euclid

Résumé

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.

Publié le : 2002-12-01
Classification: 35J30, 31B15, 31B25

@article{1085598177,
     author = {Maz'ya, Vladimir},
     title = {The Wiener test for higher order elliptic equations},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 479-512},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598177}
}

Maz’ya, Vladimir. The Wiener test for higher order elliptic equations. Duke Math. J., Tome 115 (2002) no. 1, pp.  479-512. http://gdmltest.u-ga.fr/item/1085598177/