Abstract
Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chudinovich, I., Constanda, C.: Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation, Chapman & Hall/CRC, Boca Raton – London – New York – Washington, DC (2000).
Chkadua, O., Mikhailov, S.E., Natroshvili, D.: Analysis of direct boundary–domain integral equations for a mixed BVP with variable coefficient, I: Equivalence and invertibility. Journal of Integral Equations and Applications, 21, 499–543 (2009).
Chkadua, O., Mikhailov, S.E., Natroshvili, D.: Analysis of some localized boundary–domain integral equations. Journal of Integral Equations and Applications, 21, 405–445 (2009).
Costabel, M.: Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal., 19, 613–626 (1988).
Dautray, R., Lions, J.: Mathematical Analysis and Numerical Methods for Science and Technology, vol. 4, Integral Equations and Numerical Methods, Springer, Berlin – Heidelberg – New York (1990).
Giroire, J.: Étude de Quelques Problèmes aux Limites Extérieurs et Résolution par Équations Intégrales. Thése de Doctorat d’État, Université Pierre-et-Marie-Curie (Paris-VI) (1987).
Giroire, J., Nedelec, J.: Numerical solution of an exterior Neumann problem using a double layer potential. Mathematics of Computation, 32, 973–990 (1978).
Hanouzet, B.: Espaces de Sobolev avec poids application au probleme de Dirichlet dans un demi espace. Rend. del Sem. Mat. della Univ. di Padova, XLVI, 227–272 (1971).
Lions, J.-L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, vol. 1, Springer, Berlin – Heidelberg – New York (1972).
Mäulen, J.: Lösungen der Poissongleichung und harmonishe Vektorfelder in unbeshränkten Gebieten. Math. Meth. in the Appl. Sci., 5, 233–255 (1983).
McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, Cambridge, UK (2000).
Mikhailov, S.E.: Localized boundary–domain integral formulations for problems with variable coefficients. Engineering Analysis with Boundary Elements, 26, 681–690 (2002).
Mikhailov, S.E.: Analysis of extended boundary–domain integral and integro-differential equations of some variable-coefficient BVP, in: Advances in Boundary Integral Methods — Proc. of the 5th UK Conference on Boundary Integral Methods (Editor: K. Chen), University of Liverpool Publ., Liverpool, UK, 106–125 (2005).
Mikhailov, S.E.: Analysis of united boundary–domain integro-differential and integral equations for a mixed BVP with variable coefficient. Math. Methods in Applied Sciences, 29, 715–739 (2006).
Mikhailov, S.E.: About traces, extensions and co-normal derivative operators on Lipschitz domains, in: Integral Methods in Science and Engineering: Techniques and Applications (Editors: C. Constanda, S. Potapenko), Birkhäuser, Boston, 149–160 (2008).
Mikhailov, S.E.: Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains. J. Math. Analysis and Appl., 378, 324–342 (2011).
Miranda, C.: Partial Differential Equations of Elliptic Type, Second edition, Springer, Berlin – Heidelberg – New York (1970).
Nédélec, J.-C.: Acoustic and Electromagnetic Equations, Springer-Verlag, New York (2001).
Nedelec, J., Planchard, J.: Une méthode variationelle d’éléments finis pour la résolution numérique d’un probléme extérieur dans ℝ3. RAIRO, 7, n. R3, 105–129 (1973).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Chkadua, O., Mikhailov, S.E., Natroshvili, D. (2011). Analysis of Segregated Boundary–Domain Integral Equations for Mixed Variable-Coefficient BVPs in Exterior Domains. In: Constanda, C., Harris, P. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8238-5_11
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8238-5_11
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-8237-8
Online ISBN: 978-0-8176-8238-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)