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P.A. Martin, J.D. Richardson, L.J. Gray, and J.R. Berger, On Green’s function for a three-dimensional exponentially graded elastic solid, Proc. Roy. Soc. London A458 (2002), 1931–1947.
E.E. Levi, I problemi dei valori al contorno per le equazioni lineari totalmente ellittiche alle derivate parziali, Mem. Soc. Ital. dei Sci. XL 16 (1909), 1–112.
D. Hilbert, GrundzĂĽge einer allgemeinen Theorie der linearen Integralgleichungen, Teubner, Leipzig, 1912.
C. Miranda, Partial Differential Equations of Elliptic Type, 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York, 1970.
A. Pomp, Levi functions for linear elliptic systems with variable coefficients including shell equations, Computational Mech. 22 (1998), 93–99.
A. Pomp, The Boundary-domain Integral Method for Elliptic Systems with Applications in Shells, Lect. Notes in Math. 1683, Springer-Verlag, Berlin-Heidelberg, 1998.
O. Chkadua, S.E. Mikhailov, and D. Natroshvili, Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I (submitted for publication), preprint available from http:// www.gcal.ac.uk/cms/contact/staff/sergey/CMS-MAT-PP-2004-1.pdf.
O. Chkadua, S.E. Mikhailov, and D. Natroshvili, Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. II (submitted for publication), preprint available from http:// www.gcal.ac.uk/cms/contact/staff/sergey/CMS-MAT-2004-12.pdf.
S.E. Mikhailov, Localized boundary-domain integral formulation for problems with variable coefficients, Engng. Analysis Boundary Elements 26 (2002), 681–690.
S.E. Mikhailov, Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient (submitted for publication), preprint available from http://www.gcal. ac.uk/cms/contact/staff/sergey/CMS-MAT-2004-11.pdf.
J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, vol. 1, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
M. Costabel, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988), 613–626.
R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, vol. 4: Integral Equations and Numerical Methods, Springer-Verlag, Berlin-Heidelberg, 1990.
W. McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge Univ. Press, Cambridge, 2000.
S.E. Mikhailov, On an integral equation of some boundary value problems for harmonic functions in plane multiply connected domains with nonregular boundary, Mat. Sb. 121 (1983), 533–544. (English translation: USSR Math.-Sb. 49 (1984), 525–536.)
O. Steinbach and W.L. Wendland, On C. Neumann’s method for second-order elliptic systems in domains with non-smooth boundaries, J. Math. Anal. Appl. 262 (2001), 733–748.
S.E. Mikhailov, Localized direct boundary-domain integro-differential formulations for scalar nonlinear problems with variable coefficients, J. Engng. Math. 51 (2005), 283–302.
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Mikhailov, S.E. (2006). Analysis of Boundary-domain Integral and Integro-differential Equations for a Dirichlet Problem with a Variable Coefficient. In: Constanda, C., Nashed, Z., Rollins, D. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4450-4_14
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