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Perturbation of Domains for Some Non‐Classical BVP in Elasticity
Author(s) -
Maul J.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870670602
Subject(s) - mathematics , bounded function , mathematical analysis , boundary value problem , domain (mathematical analysis) , perturbation (astronomy) , sequence (biology) , complex plane , pure mathematics , unit circle , dimension (graph theory) , physics , quantum mechanics , biology , genetics
The paper deals with two non‐classical boundary value problems of plane elastostatics, which have mechanical significance. The first problem A is studied for epitrochoids, but the second one for domains, upon which the unit circle can be mapped conformally by a rational function. The behaviour of the defect ( dimension of the kernel ) of these problems is investigated for small perturbations of the domain. In the case of problem B the following result is obtained : For a given simply connected bounded domain D of the class C m , m ≧ 2, there exists a sequence of domains { D p } p=1 ∞such that lim p→∞ n D p= ∞ ( n D p– defect of problem B in D p ). Simultaneously, the defect n D is finite, and the boundaries δD p converge to δD in the sense of C m .