Analysis of some localized boundary-domian integral equations
O. Chkadua, S. E. Mikhailov, and D. Natroshvilli
Source: J. Integral Equations Appl. Volume 21, Number 3
(2009), 407-447.
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Keywords: Partial Differential Equations; Variable coefficients; Boundary value problems; Parametrix; Localized Boundary-Domain Integral Equations; Pseudo-differential operators
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Permanent link to this document: http://projecteuclid.org/euclid.jiea/1248269703
Digital Object Identifier: doi:10.1216/JIE-2009-21-3-407
Zentralblatt MATH identifier: 05612801
Mathematical Reviews number (MathSciNet): MR2529616
References
L. Boutet de Monvel, Boundary problems for peudo-differential operators., Acta Mat., 126 (1971), 11--51.
Mathematical Reviews (MathSciNet): MR407904
Zentralblatt MATH: 0206.39401
Digital Object Identifier: doi:10.1007/BF02392024
J. Chazarain and A. Piriou, Introduction to the Theory of Linear Partial Differential Equations, Amsterdam: North-Holland (1982).
Mathematical Reviews (MathSciNet): MR678605
Zentralblatt MATH: 0487.35002
O. Chkadua, S. Mikhailov and D. Natroshvili, Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient, I: Equivalence and Invertibility, J.Integral Equat. Appl., 21 (2009), #4 (to appear).
Mathematical Reviews (MathSciNet): MR2577510
Digital Object Identifier: doi:10.1216/JIE-2009-21-4-499
Project Euclid: euclid.jiea/1262271458
--------, About Analysis of Some Localized Boundary-Domain Integral Equations for a Variable-Coefficient BVP, In: Advances in Boundary Integral Methods --- Proceedings of the 6th UK Conference on Boundary Integral Methods, (Edited by J. Trevelyan), Durham University Publ., UK, ISBN 978-0 -9535558-3-3, (2007), 291-302.
M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal., 19 (1988), 613-626.
Mathematical Reviews (MathSciNet): MR937473
Zentralblatt MATH: 0644.35037
Digital Object Identifier: doi:10.1137/0519043
R. Dautray and J. L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 4, Integral Equations and Numerical Methods, Berlin--Heidelberg: Springer (1990).
Mathematical Reviews (MathSciNet): MR1081946
Zentralblatt MATH: 0664.47002
G. Eskin, Boundary Value Problems for Elliptic Pseudodifferential Equations, Transl. of Mathem. Monographs, Vol. 52, Providence, Rhode Island: Amer. Math. Soc., (1981).
Mathematical Reviews (MathSciNet): MR623608
G. Grubb, Functional Calculus of Pseudodifferential Boundary Problems, Boston: Birkhäuser (1986).
Mathematical Reviews (MathSciNet): MR885088
Zentralblatt MATH: 0844.35002
P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, Boston--London--Melbourne, (1985).
Mathematical Reviews (MathSciNet): MR775683
Zentralblatt MATH: 0695.35060
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol. 1. Springer, Berlin-Heidelberg-New York, (1972).
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, UK, (2000).
Mathematical Reviews (MathSciNet): MR1742312
Zentralblatt MATH: 0948.35001
S.E. Mikhailov, Localized boundary--domain integral formulation for problems with variable coefficients, Int. J. Engineering Analysis with Boundary Elements, 26 (2002), 681-690.
--------, Analysis of extended boundary-domain integral and integro-differential equations of some variable-coefficient BVP, In: Ke Chen (Edr.), Advances in Boundary Integral Methods --- Proceedings of the 5th UK Conference on Boundary Integral Methods, Liverpool, UK. University of Liverpool Publ., (2005), 106-125.
--------, Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient. Math. Methods in Applied Sciences, 29 (2006), 715-739.
Mathematical Reviews (MathSciNet): MR2213096
Zentralblatt MATH: 1146.35031
Digital Object Identifier: doi:10.1002/mma.706
--------, About traces, extensions and co-normal derivative operators on Lipschitz domains, In: C. Constanda and S. Potapenko, eds., Integral Methods in Science and Engineering: Techniques and Applications, Birkhäuser, (2007), 149-160.
Mathematical Reviews (MathSciNet): MR2389522
Digital Object Identifier: doi:10.1007/978-0-8176-4671-4_18
Zentralblatt MATH: 05659389
S. E. Mikhailov, I. S. Nakhova, Mesh-based numerical implementation of the localized boundary-domain integral equation method to a variable-coefficient Neumann problem, J. Engineering Math., 51 (2005), 251-259.
Mathematical Reviews (MathSciNet): MR2136853
Zentralblatt MATH: 1073.65137
Digital Object Identifier: doi:10.1007/s10665-004-6452-0
C. Miranda, Partial Differential Equations of Elliptic Type, 2-nd ed. Springer, Berlin -- Heidelberg -- New York, (1970).
Mathematical Reviews (MathSciNet): MR284700
Zentralblatt MATH: 0198.14101
A. Pomp, The Boundary-Domain Integral Method for Elliptic Systems. With Applications in Shells, Lecture Notes in Mathematics, v. 1683, Springer, Berlin - Heidelberg, (1998).
Mathematical Reviews (MathSciNet): MR1631644
Zentralblatt MATH: 0894.65058
J. Sladek, V. Sladek V, S. N. Atluri (2000), Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties, Comput. Mech., 24, 456-462.
J. Sladek, V. Sladek V, Ch. Zhang, Local integro-differential equations with domain elements for the numerical solution of partial differential equations with variable coefficients, J. Eng. Math., 51 (2005), 261-282.
Mathematical Reviews (MathSciNet): MR2136854
Zentralblatt MATH: 1073.65138
Digital Object Identifier: doi:10.1007/s10665-004-3692-y
A. E. Taigbenu, The Green Element Method, Kluwer, (1999).
V.S. Vladimirov, Generalized Functions of Mathematical Physics, Nauka, Moscow, (1976).
Mathematical Reviews (MathSciNet): MR450966
T. Zhu, J.-D. Zhang, S. N. Atluri, A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach, Comput. Mech., 21 (1998), 223-235.
Mathematical Reviews (MathSciNet): MR1633729
--------, A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems, Engng. Anal. Bound. Elem., 23 (1999), 375-389.
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