 03459 Yu. Netrusov and Yu. Safarov
 Weil asymptotic formula for the Laplacian on domains with rough boundaries
(105K, LaTeX)
Oct 7, 03

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We study asymptotic distribution of eigenvalues of the Laplacian
on a bounded domain in $R^n$. Our main results include an
explicit remainder estimate in the Weyl formula for the Dirichlet
Laplacian on an arbitrary bounded domain, sufficient conditions
for the validity of the Weyl formula for the Neumann Laplacian on
a domain with continuous boundary in terms of smoothness of the
boundary and a remainder estimate in this formula. In particular,
we show that the Weyl formula holds true for the Neumann Laplacian
on a $\,\Lip_\alpha$domain whenever $(d1)/\alpha<d$, prove
that the remainder in this formula is
$O(\lambda^{(d1)/\alpha})$ and give an example where the
remainder estimate $O(\lambda^{(d1)/\alpha})$ is order sharp.
We use a new version of variational technique which does not
require the extension theorem.
 Files:
03459.src(
03459.comments ,
03459.keywords ,
Netr_1003.tex )