Stress potentials on \(C^ 1\) domains
type: Item
instance of: scholarly article
title: Stress potentials on \(C^ 1\) domains
zbMATH Open document ID: 0633.73005
DOI: 10.1016/0022-247X(87)90162-4
author: B. George
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The paper is a continuation of the authors' earlier work [Ark. Mat. 23, 217-240 (1985; Zbl 0602.35028) and Indiana Univ. Math. J. 32, 635-685 (1983; Zbl 0534.31003)] relating to the Dirichlet problem and adjoint boundary value problems for the biharmonic equation on \(C^ 1\)-domains in the plane. The concept of modified lower order potential introduced by the authors is used for determining the stress function from the boundary stresses. The results obtained provide a point-wise solution to the Neumann-type boundary value problem for a biharmonic equation. It is shown that the solution of the boundary value problem for a biharmonic equation can be obtained with boundary data in the sub-space \(L^ q\times L^ q(\Omega)\) and with the boundary values obtained nontangentially point-wise almost everywhere. As a matter of fact the classical elasto-static problem of obtaining interior stress from the prescribed stress on the boundary has been solved and the solution of biharmonic problem on \(C^ 1\) domain with data in \(L^ p\) for \(1<p<\infty\) has been obtained.
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 31A25
zbMATH DE Number: 4031093
zbMATH Keywords: C(sup 1)-domains
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: biharmonic equation
zbMATH Keywords: modified lower order potential
zbMATH Keywords: point-wise solution
zbMATH Keywords: Neumann-type boundary value problem
zbMATH Keywords: elasto-static problem
zbMATH Keywords: interior stress
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4031093