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Abstract Uniform asymptotic approximations of Green's kernels for the harmonic mixed and Neumann boundary value problems in domains with singularly perturbed boundaries are obtained. We consider domains with small holes (in particular, cracks) or inclusions. Formal asymptotic algorithms are supplied with rigorous estimates of the remainder terms.
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References
Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer, Berlin-Heidelberg-New York (1983)
Hadamard, J.: Sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées. Mémoire couronné en 1907 par l'Académie des Sciences 33, no 4, 515–629 (1907)
Landkof, N.S.: Foundations of Modern Potential Theory. Spinger, Berlin-Heidelberg-New York (1972)
Maz'ya, V.: Sobolev Spaces. Spinger, Berlin-Heidelberg-New York (1985
Maz'ya, V., Movchan, A.: Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains. C. R. Acad. Sci. Paris, Ser. Math. 343, 185–190 (2006)
Maz'ya, V., Movchan, A.: Uniform asymptotic formulae for Green's functions in singularly perturbed domains. J. Comp. Appl. Math.. 228, 194–206 (2007)
Maz'ya, V.G., Plamenevskii, B.A.: Estimates in L p and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary. Transl., Ser. 2, Am. Math. Soc. 123, 1–56 (1984)
Pólya, G., Szegö, G.: Isoperimetric Inequalities in Mathematical Physics. Princeton (1951)
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Maz'ya, V., Movchan, A. (2009). Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions. In: Isakov, V. (eds) Sobolev Spaces in Mathematics III. International Mathematical Series, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85652-0_6
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DOI: https://doi.org/10.1007/978-0-387-85652-0_6
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