V. I. Astakhov, “Additivity of the Space of Densities of Simple-Layer Potentials with a Finite Dirichlet Integral and Integrability of Normal Derivatives of Harmonic <nobr>$W_2^1$</nobr>-Functions on Lipschitz Surfaces”, Mat. Zametki, 2011, Volume 90, Issue 5,Pages <nobr>659

Additivity of the Space of Densities of Simple-Layer Potentials with a Finite Dirichlet Integral and Integrability of Normal Derivatives of Harmonic $W_2^1$-Functions on Lipschitz Surfaces

V. I. Astakhov

Southern Research Center of the Russian Academy of Sciences

Abstract: We prove that the normal derivatives of piecewise harmonic functions and the densities of surface simple-layer potentials with a finite Dirichlet integral belong to the Lebesgue space on Lipschitz surfaces.

Keywords: simple-layer potential, normal derivative, integrability, Lipschitz surface, harmonic function, Lebesgue measure, Dirichlet integral.

UDC: 517.956.224

Received: 15.07.2009

DOI: 10.4213/mzm8758