Boundary value problems in elastostatics with singular data
type: Item
instance of: scholarly article
title: Boundary value problems in elastostatics with singular data
zbMATH Open document ID: 1481.74067
author: Giulio Starita
author: Alfonsina Tartaglione
published in: Lithuanian Mathematical Journal
publication date: 2021-05-06T00:00:00Z
review text: The present paper deals with well-posedness of three-dimensional BVPs of elasticity, in the isotropic case, under weak regularity assumptions on the boundary data, e.g., Borel measurability of boundary data or the presence of concentrated loads. The paper consists of six sections and references with 21 sources. Section 1 is intended to motivate investigations carried out in the paper, it contains notation and a brief survey of classical results as well. Section 2 provides a detailed exposition of the single-layer and double-layer potentials with densities from \(L^1\). Section 3 is devoted to the Dirichlet-Neumann-Robin problem for bounded or exterior domains of class \(C^k\), \(k\ge 2\). Section 4 deals with mixed problems, and the existence of a unique very weak solution is established. Section 5 is devoted to the Dirichlet-Neumann-Robin problem in bounded or exterior domains of class \(C^{1,\alpha}\). Existence of a unique solution expressed by a simple-layer potential with density from \(L^q\) is proved. For the exterior domain the existence of a unique solution expressed by a simple-layer potential with density from \(W^{-1,q}\) is also proved. Section 6 deals with displacement problem in a bounded domain of class \(C^1\) and in exterior domains either of class \(C^1\) or of class \(C^2\).
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 7345274
zbMATH Keywords: linear three-dimenstonal elastostatics
zbMATH Keywords: double-layer potential
zbMATH Keywords: boundary value problem
zbMATH Keywords: weak solution
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: singular data
reviewed by: G. Jaiani
MaRDI profile type: Publication
full work available at URL: s10986-020-09489-3
OpenAlex ID: W3045792019
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DOI: 10.1007/S10986-020-09489-3
description: scientific article; zbMATH DE number 7345274