Integral representations and boundary value problems for a second-order elliptic system with a singular point
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For a second-order elliptic system with a singular point, we obtain integral representations and inversion formulas for the case in which the singular point is an interior point of the domain. In the integral representations, we clearly extract the singular part of the solutions, which permits one to study the asymptotics of the solutions as r → 0. In addition, we give a well-posed statement of a number of boundary value problems.
KeywordsSingular Point Integral Representation Interior Point Elliptic System Inversion Formula
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- 1.Bitsadze, A.V., Nekotorye klassy uravnenii v chastnykh proizvodnykh (Some Classes of Partial Differential Equations), Moscow: Nauka, 1981.Google Scholar
- 3.Usmanov, Z.D., Obobshchennye sistemy Koshi-Rimana s singulyarnoi tochkoi (Generalized Cauchy-Riemann Systems with a Singular Point), Dushanbe, 1992.Google Scholar
- 4.Radzhabov, N.R., Vvedenie v teoriyu differentsial’nykh uravnenii v chastnykh proizvodnykh so sverkhsingulyarnymi koeffitsientami (Introduction to the Theory of Partial Differential Equations with Super-Singular Coefficients), Dushanbe, 1992.Google Scholar
- 5.Korn, G.A. and Korn, T.M., Mathematical Handbook for Scientists and Engineers, New York: McGraw Hill, 1968. Translated under the title Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov, Moscow: Nauka, 1984.Google Scholar