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Published in:
1992 | OriginalPaper | Chapter
The Spectral Radius of the Classical Layer Potentials on Convex Domains
Authors : Eugene Fabes, Mark Sand, Jin Keun Seo
Published in: Partial Differential Equations with Minimal Smoothness and Applications
Publisher: Springer New York
Included in: Professional Book Archive
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Let D denote a bounded Lipschitz domain in Rn. For almost every (with respect to surface measure dσ)Q ∈∂D the exterior normal NQ at Q exists. The solution u to the Dirichlet problem, $$\Delta u = 0 \text{ i}n \ \ D, \ \ u \vert_{\partial D} = g$$, with g ∈L2(∂D,dσ) can be represented in the form of the classical double layer potential $$u(X) = \frac{1}{\omega_n} \int\limits_{\partial D} \frac{N_Q\circ(Q - X)}{\left\vert X - Q \right\vert^n}[((1/2)I + K)^{-1}g](Q)d\sigma(Q)$$.