A general theory of hypersurface potentials
type: Item
instance of: scholarly article
title: A general theory of hypersurface potentials
zbMATH Open document ID: 0855.31004
DOI: 10.1007/BF01759253
author: A. Cialdea
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1997-02-03T00:00:00Z
review text: The author investigates hypersurface potentials with general kernels. Particularly, he proves \[ \begin{aligned} \lim_{t\to +0} \int_{\mathbb{R}^{n-1}} \varphi (x) K(x, t)dx &= \gamma \varphi (0)+ \int_{\mathbb{R}^{n-1}} \varphi (x) K(x, 0) dx,\\ \lim _{\substack{ x\to x_0\\ x\in \nu_{x_0} }}\;\int_\Sigma \varphi (y) {\partial \over {\partial \nu_{x_0}}} h(x- y) d\sigma_y &= \gamma (x_0) \varphi (x_0)+ \int_\Sigma \varphi (y) {\partial \over {\partial \nu_{x_0}}} h(x_0- y) d\sigma_y, \end{aligned} \] where \(\varphi\) belongs to the Hölder's class, Lyapunov's manifold \(\Sigma\) is the boundary of a bounded domain, the values \(\gamma\) and \(\gamma (x_0)\) are defined by the kernels, \(\nu_{x_0}\) is the inner normal at the point \(x_0\in \Sigma\), \(K(x, t)\) and \(h(x)\) are kernels of special classes. Potentials of functions of the class \(L_p\) and potentials of measures are considered as well.
Mathematics Subject Classification ID: 31B25
Mathematics Subject Classification ID: 35B15
zbMATH DE Number: 878441
zbMATH Keywords: singular integral
zbMATH Keywords: homogeneous kernel
zbMATH Keywords: Lyapunov's manifold
zbMATH Keywords: hypersurface potentials with general kernels
zbMATH Keywords: potentials of measures
MaRDI profile type: Publication
cites work: On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
cites work: Q5335574
cites work: On the existence of certain singular integrals
cites work: On Singular Integrals
cites work: Q3831325
cites work: Elastostatics with non absolutely continuous data
cites work: Teoremi di completezza sulla frontiera di un dominio per taluni sistemi di funzioni
cites work: Q3276064
cites work: Q3264933
cites work: Q3847188
cites work: Q5632845
cites work: Q4115521
cites work: Solution of Boundary Value Problems by Integral Equations of the First Kind
cites work: Q4193022
cites work: Q5518064
cites work: Q4179263
description: scientific article; zbMATH DE number 878441