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Summary: SPECTRAL CHARACTERIZATION OF THE TRACE SPACES Hs
().
GILES AUCHMUTY
Abstract. The spaces Hs
() are described via Steklov eigenfunction expansions.
This characterization provides explicit formulae for the inner products, norms and al-
lows the description of explicit orthonormal bases for these spaces. It uses a special inner
product on H1
(), and properties of the harmonic Steklov eigenfunctions on the region.
This approach only requires the boundary of the region be Lipschitz and generalizes the
classical definitions that are used when the boundary is a smooth manifold.
1. Introduction
This paper develops a spectral characterization of Hilbert trace spaces on Lipschitz
regions in Rn
. The description uses Steklov eigenfunction expansions and provides explicit
formulae for the inner products, norms and orthonormal bases.
The approach used here is intrinsic and is based on the use of special inner products
and related decompositions for H1
(). The Steklov eigenfunctions then simultaneously
provide orthogonal sets in H1
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