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On the boundary value problem of the biharmonic operator on domains with angular corners. (English) Zbl 0445.35023


MSC:

35D10 Regularity of generalized solutions of PDE (MSC2000)
35B45 A priori estimates in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35B40 Asymptotic behavior of solutions to PDEs
74G70 Stress concentrations, singularities in solid mechanics
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References:

[1] Agranoviš, Elliptic boundary value problems depending on a parameter, Soviet Math. Dokl. 4 pp 325– (1963)
[2] Blum , H. 1979
[3] Grisvard, Numerical Solution of Partial Differential Equations, SYNSPADE III, pp pp 207– (1976)
[4] Karp, The elastic-field behavior in the neighborhood of a crack of arbitrary angle, Comm. Pure Appl. Math. 15 pp 413– (1962) · Zbl 0166.20705
[5] Kellogg, A regularity result for the Stokes problem in a convex polygon, J. Functional Anal. 21 pp 397– (1976) · Zbl 0317.35037
[6] Knightly, An existence theorem for the von Kármán equations, Arch. Rational Mech. Anal. 27 pp 233– (1967) · Zbl 0162.56303
[7] Kondrat’ev, Boundary problems for parabolic equations in closed domains, Trans. Moscow Math. Soc. 15 pp 450– (1966)
[8] Kondrat’ev, Boundary problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc. 16 pp 227– (1967)
[9] Kondrat’ev, Asymptotic of a solution of the Navier-Stokes equation near the angular part of the boundary, J. Appl. Math. Mech. 31 pp 125– (1967)
[10] Kondrat’ev, The smoothness of a solution of Dirichlet’s problem for 2nd order elliptic equations in a region with a piecewise smooth boundary, Differential Equations 6 pp 1831– (1970)
[11] Kufner, Lösungen des Dirichletschen Problems für elliptische Differentialgleichungen in Räumen mit Belegungsfunktionen, Czechoslovak Math. J. 15 pp 621– (1965) · Zbl 0148.35603
[12] Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow (1962) · Zbl 0184.52603
[13] Melzer, Spannungskonzentrationen in Eckpunkten der Kirchhoffschen Platte, Der Bauingenieur (1980)
[14] Moffat , H. K. The asymptotic behaviour of solutions of the Navier-Stokes equations near sharp corners 1979
[15] Nešas, Les Méthodes Directes en Théorie des Equations Elliptiques (1967)
[16] Neumark, Lineare Differentialoperatoren (1967)
[17] Seif, On the Green’s function for the biharmonic equation in an infinite wedge, Trans. Amer. Math. Soc. 182 pp 241– (1973) · Zbl 0271.31005
[18] Williams , M. L. Proc. First U. S. Nat. Congr. of Appl. Mech. 1951 325 329
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