Layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains
Author:
Jeff E. Lewis
Journal:
Trans. Amer. Math. Soc. 320 (1990), 5376
MSC:
Primary 35J25; Secondary 35Q20, 35S05, 45K05, 47A53, 47G05, 73C02, 76D07
MathSciNet review:
1005935
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Abstract: The symbolic calculus of pseudodifferential operators of Mellin type is applied to study layer potentials on a plane domain whose boundary is a curvilinear polygon. A "singularity type" is a zero of the determinant of the matrix of symbols of the Mellin operators and can be used to calculate the "bad values" of for which the system is not Fredholm on . Using the method of layer potentials we study the singularity types of the system of elastostatics in a plane domain whose boundary is a curvilinear polygon. Here and . When , the system is the Stokes system of hydrostatics. For the traction double layer potential, we show that all singularity types in the strip lie in the interval so that the system of integral equations is a Fredholm operator of index 0 on for all , . The explicit dependence of the singularity types on and the interior angles of is calculated; the singularity type of each corner is independent of iff the corner is nonconvex.
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 E. B. Faves, C. E. Kenig, and G. C. Verchota, The Dirichlet problem for the Stokes system on Lipschitz domain, Duke Math. J. 57 (1988), 769795. MR 975121 (90d:35258)
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 D. Vasilopoulos, On the determination of higher order terms of singular elastic stress fluids near corners, Numer. Math. 53 (1988), 5196. MR 946369 (89h:65193)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199010059355
PII:
S 00029947(1990)10059355
Article copyright:
© Copyright 1990
American Mathematical Society
