Free Access
Issue
ESAIM: M2AN
Volume 40, Number 3, May-June 2006
Page(s) 553 - 595
DOI https://doi.org/10.1051/m2an:2006022
Published online 22 July 2006
  1. M.S. Agranovich and M.I. Vishik, Elliptic problems with the parameter and parabolic problems of general type. Uspekhi Mat. Nauk 19 (1963) 53–161 (English transl.: Russ. Math. Surv. 19 (1964) 53–157). [Google Scholar]
  2. N.Kh. Arutyunyan and V.B. Kolmanovskii, The theory of creeping heterogeneous bodies. Nauka, Moscow (1983) 336. [Google Scholar]
  3. N.Kh. Arutyunyan, S.A. Nazarov and B.A. Shoikhet, Bounds and the asymptote of the stress-strain state of a threedimensional body with a crack in elasticity theory and creep theory. Dokl. Akad. Nauk SSSR 266 (1982) 1361–1366 (English transl.: Sov. Phys. Dokl. 27 (1982) 817–819). [MathSciNet] [Google Scholar]
  4. N.Kh. Arutyunyan, A.D. Drozdov and V.E. Naumov, Mechanics of growing visco-elasto-plastic bodies. Nauka, Moscow (1987) 472. [Google Scholar]
  5. C. Atkinson and J.P. Bourne, Stress singularities in viscoelastic media. Q. J. Mech. Appl. Math. 42 (1989) 385–412. [CrossRef] [Google Scholar]
  6. C. Atkinson and J.P. Bourne, Stress singularities in angular sectors of viscoelastic media. Int. J. Eng. Sci. 28 (1990) 615–650. [CrossRef] [Google Scholar]
  7. J.P. Bourne and C. Atkinson, Stress singularities in viscoelastic media. II. Plane-strain stress singularities at corners. IMA J. Appl. Math. 44 (1990) 163–180. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Costabel and M. Dauge, Construction of corner singularities for Agmon-Douglis-Nirenberg elliptic systems. Math. Nachr. 162 (1993) 209–237. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Costabel and M. Dauge, Crack singularities for general elliptic systems. Math. Nachr. 235 (2002) 29–49. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Costabel, M. Dauge and R. Duduchava, Asymptotics without logarithmic terms for crack problems. Comm. Partial Differential Equations 28 (2003) 869–926. [CrossRef] [MathSciNet] [Google Scholar]
  11. R. Duduchava and W.L. Wendland, The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems. Integr. Equat. Oper. Th. 23 (1995) 294–335. [CrossRef] [Google Scholar]
  12. R. Duduchava, A.M. Sändig and W.L. Wendland, Interface cracks in anisotropic composites. Math. Method. Appl. Sci. 22 (1999) 1413–1446. [CrossRef] [Google Scholar]
  13. J. Dundurs, Effect of elastic constants on stress in composite under plane deformations. J. Compos. Mater. 1 (1967) 310. [Google Scholar]
  14. G. Gripenberg, S.-O. Londen and O. Staffans, Volterra Integral and Functional equations. Cambridge Univ. Press, Cambridge (1990). [Google Scholar]
  15. V.A. Kondratiev, Boundary problems for elliptic equations in domains with conical or angular points. Trudy Moskov. Mat. Obshch. 16 (1967) 209–292 (English transl.: Trans. Moscow Math. Soc. 16 (1967) 227–313). [Google Scholar]
  16. V.A. Kondratiev and O.A. Oleinik, Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities. Uspehi Mat. Nauk 43 (1988) 55–98 (English transl.: Russ. Math. Surv. 43 (1988) 65–119). [Google Scholar]
  17. V.A. Kozlov, V.G. Maz'ya and J. Rossmann, Elliptic boundary value problems in domains with point singularities. Amer. Math. Soc., Providence (1997). [Google Scholar]
  18. M.A. Krasnosel'skii, G.M. Vainikko and P.P. Zabreiko, Approximate solutions to integral equations. Nauka, Moscow (1969) 455. [Google Scholar]
  19. V.G. Maz'ya and B.A. Plamenevskii, Weighted spaces with nonhomogeneous norms and boundary value problems in domains with conical points. In: Elliptische Differentialgleichungen (Meeting in Rostock, 1977), Wilhelm-Pieck-Univ., Rostock (1978) 161–189 (English transl.: Amer. Math. Soc. Transl. Ser. 2 123 (1984) 89–107). [Google Scholar]
  20. V.G. Maz'ya and B.A. Plamenevskii, The coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points. Math. Nachr. 76 (1997) 29–60 (English transl.: Amer. Math. Soc. Transl. Ser. 2 123 (1984) 57–88). [Google Scholar]
  21. S.E. Mikhailov, Singularities of stresses in a plane hereditarily-elastic aging solid with corner points. Mech. Solids (Izv. AN SSSR. MTT) 19 (1984) 126–139. [Google Scholar]
  22. S.E. Mikhailov, Singular stress behavior in a bonded hereditarily-elastic aging wedge. Part. I: Problem statement and degenerate case. Math. Method. Appl. Sci. 20 (1997) 13–30. [CrossRef] [Google Scholar]
  23. S.E. Mikhailov, Singular stress behavior in a bonded hereditarily-elastic aging wedge. Part. II: General heredity. Math. Method. Appl. Sci. 20 (1997) 31–45. [CrossRef] [Google Scholar]
  24. S.A. Nazarov, Vishik-Lyusternik method for elliptic boundary-value problems in regions with conical points. 1. The problem in a cone. Sibirsk. Mat. Zh. 22 (1981) 142–163 (English transl.: Siberian Math. J. 22 (1982) 594–611). [Google Scholar]
  25. S.A. Nazarov, Weight functions and invariant integrals. Vychisl. Mekh. Deform. Tverd. Tela. 1 (1990) 17–31. (Russian) [Google Scholar]
  26. S.A. Nazarov, Self-adjoint boundary value problems. The polynomial property and formal positive operators. St.-Petersburg Univ., Probl. Mat. Anal. 16 (1997) 167–192. (Russian) [Google Scholar]
  27. S.A. Nazarov, The interface crack in anisotropic bodies. Stress singularities and invariant integrals. Prikl. Mat. Mekh. 62 (1998) 489–502 (English transl.: J. Appl. Math. Mech. 62 (1998) 453–464). [Google Scholar]
  28. S.A. Nazarov, The polynomial property of self-adjoint elliptic boundary-value problems and the algebraic description of their attributes. Uspekhi mat. nauk 54 (1999) 77–142 (English transl.: Russ. Math. Surv. 54 (1999) 947–1014). [Google Scholar]
  29. S.A. Nazarov and B.A. Shoikhet, Asymptotic behavior of the solution of a certain integro-differential equation near an angular point of the boundary. Mat. Zametki. 33 (1983) 583–594 (English transl.: Math. Notes 33 (1983) 300–306). [MathSciNet] [Google Scholar]
  30. S.A. Nazarov and B.A. Plamenevskii, Neumann problem for selfadjoint elliptic systems in a domain with piecewise smooth boundary. Trudy Leningrad. Mat. Obshch. 1 (1990) 174–211 (English transl.: Amer. Math. Soc. Transl. Ser. 2 155 (1993) 169–206). [MathSciNet] [Google Scholar]
  31. S.A. Nazarov and B.A. Plamenevsky, Elliptic problems in domains with piecewise smooth boundaries. Walter de Gruyter, Berlin, New York (1994) 525. [Google Scholar]
  32. S.A. Nazarov, L.P. Trapeznikov and B.A. Shoikhet, On the correspondence principle in the plane creep problem of aging homogeneous media with developing slits and cavities. Prikl. Mat. Mekh. 51 (1987) 504–512 (English transl.: J. Appl. Math. Mech. 51 (1987) 392–399). [Google Scholar]
  33. J. Nečas, Les méthodes directes en théorie des équations elliptiques. Masson-Academia, Paris-Prague (1967). [Google Scholar]
  34. A.C. Pipkin, Lectures on viscoelasticity theory. Springer, NY (1972) 180. [Google Scholar]
  35. G.S. Vardanyan and V.D. Sheremet, On certain theorems in the plane problem of the creep theory. Izvestia AN Arm. SSR. Mechanics 4 (1973) 60–76. [Google Scholar]
  36. V.P. Zhuravlev, S.A. Nazarov and B.A. Shoikhet, Asymptotics of the stress-strain state near the tip of a crack in an inhomogeneously aging bodies. Dokl. Akad. Nauk Armenian SSR 74 (1982) 26–29. (Russian) [Google Scholar]
  37. V.P. Zhuravlev, S.A. Nazarov and B.A. Shoikhet, Asymptotics near the tip of a crack of the state of stress and strain of inhomogeneously aging bodies. Prikl. Mat. Mekh. 47 (1983) 200–208 (English transl.: J. Appl. Math. Mech. 47 (1984) 162–170). [Google Scholar]

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