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

Geodesic

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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

Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 659-664

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Résumé

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, Dirichlet integral.
Mots-clés : Lebesgue measure

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     author = {V. I. Astakhov},
     title = {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}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {659--664},
     publisher = {mathdoc},
     volume = {90},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a1/}
}

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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 $W_2^1$-Functions on Lipschitz Surfaces. Matematičeskie zametki, Tome 90 (2011) no. 5, pp. 659-664. http://geodesic.mathdoc.fr/item/MZM_2011_90_5_a1/