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Crack singularities for general elliptic systems. (English) Zbl 1094.35038

General elliptic systems in a domain with a crack are considered. The method of investigation is based on reducing it to the investigation of characteristic matrices. The singularity exponents for general elliptic systems when boundary conditions on both sides of a crack are the same and for a self-adjoint strongly coercive systems when the boundary conditions on both sides of a crack are not the same.

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
74B05 Classical linear elasticity
74A45 Theories of fracture and damage
74G60 Bifurcation and buckling
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[1] Agmon, Comm. Pure Appl. Math. 17 pp 35– (1964) · Zbl 0123.28706
[2] Agranovich, Russian Math. Surveys 19 pp 53– (1964) · Zbl 0137.29602
[3] Costabel, Math. Nachr. 162 pp 209– (1993) · Zbl 0802.35032
[4] Costabel, Arch. Rational Mech. Anal. 151 pp 221– (2000) · Zbl 0968.35113
[5] : Elliptic Boundary Value Problems in Corner Domains - Smoothness and Asymptotics of Solutions, Lecture Notes in Mathematics 1341, Springer-Verlag, Berlin, 1988
[6] Duduchava, Math. Nachr. 191 pp 83– (1998) · Zbl 0901.73016
[7] Duduchava, Integral Equations Operator Theory 23 pp 294– (1995) · Zbl 1126.35368
[8] : Boundary Value Problems in Non-Smooth Domains, Pitman, London, 1985
[9] Grisvard, Arch. Rational Mech. Anal. 107 pp 157– (1989) · Zbl 0706.73013
[10] Kondrat’ev, Trans. Moscow Math. Soc. 16 pp 227– (1967)
[11] Kozlov, Leningrad Math. J. 4 pp 967– (1990)
[12] Kozlov, Funktsional. Anal. i Prilozhen. 22 pp 38– (1988)
[13] and : Problèmes aux Limites non Homogènes et Applications, Dunod, Paris, 1968
[14] Nazarov, Vychisl. Mekh. Deform. Tverd. Tela 1 pp 17– (1990)
[15] and : Boundary Value Problems in Boutet de Monvel’s Algebra for Manifolds with Conical Singularities. II. In: Boundary Value Problems, Schrödinger Operators, Deformation Quantization, pp. 70-205, Akademie Verlag, Berlin, 1995 · Zbl 0847.35156
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