On boundary integral equations of the first kind for the bi-laplacian in a polygonal plane domain

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1. [1] A. Avantaggiati - M. Troisi, Spazi di Sobolev con peso e problemi ellittici in un angolo, I, II, III, Ann. Mat. Pura Appl., 95 (1973), pp. 361-408; Ann. Mat. Pura Appl., 97 (1973), pp. 207-252; Ann. Mat. Pura Appl., 99 (1974), pp. 1-51. MR355319
2. [2] J.D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell Publishing Comp., Waltham, Mass. (1968). Zbl0162.12602MR246537
3. [3] H.O. Cordes - E. Herman, Singular integrals on the half-line, Proc. Nat. Acad. Sci., 56 (1966), pp. 1668-1673. Zbl0152.14201MR213918
4. [4] M. Costabel, Singular integral operators on curves with corners, Integral Equations Oper. Theory, 3 (1980), pp. 323-349. Zbl0445.45025MR580713
5. [5] M. Costabel - E. Stephan, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, THD-preprint Nr. 593, Darmstadt (1981), to appear in Banach Center Publications. Zbl0655.65129MR874845
6. [6] M. Costabel - E. Stephan, The boundary integral method for a mixed boundary value problem in a polygonal domain, Advances in Computer Methods for Partial Diff. Equations IV, IMACS (1981), pp. 300-304. 
7. [7] G.I. Eskin, Boundary value problems for elliptic pseudo-differential equations, A.M.S. (Transl. of Math. Mon., 52), Providence, Rhode Island (1981). Zbl0458.35002MR623608
8. [8] E.B. Fabes - M. Jodeit - J.E. Lewis, On the spectra of a Hardy Kernel, J. Functional Analysis, 21 (1976), pp. 187-194. Zbl0321.47038MR394311
9. [9] E.B. Fabes - M. Jodeit - J.E. Lewis, Double layer potentials for domains with corners and edges, Indiana Univ. Math. J., 26 (1977), pp. 95-114. Zbl0363.35010MR432899
10. [10] G. Fichera, Linear elliptic equations of higher order in two independent variables and singular integral equations, Proc. Conf. partial diff. equations and cont. mechanics, Univ. Wisconsin Press, (1961), pp. 55-80. Zbl0111.29602MR156084
11. [11] J. Giroire, Formulation variationelle par équations intégrales de problèmes aux limites extérieurs, Rapport Interne École Polytechnique6 (1976). 
12. [12] I. Gohberg - N. Krupnik, Einführung in die Theorie der eindimensionalen singulären Integraloperatoren, Birkhäuser Verlag, Basel (1979). Zbl0413.47040MR545507
13. [13] P. Grisvard, Boundary value problems in non-smooth domains, Univ. Maryland, Lecture Notes19 (1980). 
14. [14] G.C. Hsiao - P. Kopp - W.L. Wendland, Some applications of a Galerkin-collocation method for integral equations of the first kind, THD-preprint Nr.768, Darmstadt (1983), to appear in Math. Meth. in the Appl. Sci.. Zbl0546.65091
15. [15] G.C. Hsiao - R. Maccamy, Solution of boundary value problems by integral equations of the first kind, SIAM Rev., 15 (1973), pp. 687-705. Zbl0235.45006MR324242
16. [16] G.C. Hsiao - W.L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl., 58 (1977), pp. 449-481. Zbl0352.45016MR461963
17. [17] M.A. Jaswon - G.T. Symm, Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, New York - San Francisco - London (1977). Zbl0414.45001MR499236
18. [18] V.A. Kondratiev, Boundary problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc., 16 (1967), pp. 227-313. Zbl0194.13405
19. [19] J.E. Lewis - C. Parenti, Pseudodifferential operators and Hardy Kernels on Lp(R+), Ann. Scuola Norm. Sup. Pisa, Ser. IV, 7 (1980), pp. 481-503. Zbl0466.35071MR597548
20. [20] J.L. Lions - E. Magenes, Non-Homogeneous Boundary Value Problems and Applications I, Springer-Verlag, Berlin - Heidelberg - New York (1972). Zbl0223.35039
21. [21] R. Lozi, Résultats numériques de régularité du problème de Stokes et du Laplacien itéré dans un Polygon, preprint Univ. Nice (1978). Zbl0385.65025MR509976
22. [22] H. Melzer - R. Rannacher, Spannungskonzentrationen in Eckpunkten der Kirschhoffschen Platte, Bauingenieur, 55 (1980), pp. 181-184. 
23. [23] J Nečas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris (1967). MR227584
24. [24] B.A. Plamenevskii, On an algebra of pseudodifferential operators in spaces with weighted norms, Math. USSR-Sb., 34 (1978), pp. 841-865. Zbl0414.35079
25. [25] M. Reed - B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York - San Francisco - London (1975). Zbl0308.47002MR751959
26. [26] T.B. Seif, On the Green's function for the biharmonic equation in an infinite wedge, Trans. Amer. Math. Soc., 182 (1973), pp. 241-260. Zbl0271.31005MR325989
27. [27] E. Shamir, Mixed boundary value problems for elliptic equations in the plane —the Lp-theory, Ann. Scuola Norm. Sup. Pisa, Ser. III, 17 (1963), pp. 117-139. Zbl0117.07002MR157089
28. [28] E. Stephan, Conform and mixed finite element schemes for the Dirichlet problem for the bilaplacian in plane domains with corners, Math. Meth. in the Appl. Sci., 1 (1979), pp. 354-382. Zbl0439.65091MR548946
29. [29] E. Stephan - W.L. Wendland, Remarks to Galerkin and least squares methods with finite elements for general elliptic problems, Manuscripta geodaetica, 1 (1976), pp. 93-123. Zbl0353.65067
30. [30] E. Stephan - W.L. Wendland, Boundary element method for membrane and torsion crack problems, Comput. Methods Appl. Mech. Engrg, 36 (1983), pp. 331-358. Zbl0488.73096MR691059
31. [31] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam (1977) . Zbl0383.35057MR769654
32. [32] H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland Publishing Company, Amsterdam - New York - Oxford (1978). Zbl0387.46032MR503903
33. [33] W.L. Wendland, On the asymptotic convergence of some boundary element methods, Mathematics of Finite Elements and Appl. Iv, Mafelap1981, Academic Press, London (1982), pp. 281-312. Zbl0561.65086
34. [34] W.L. Wendland - E. Stephan - G.C. Hsiao, On the integral equation method for the plane mixed boundary value problem of the Laplacian, Math. Meth. in the Appl. Sci., 1 (1979), pp. 265-321. Zbl0461.65082MR548943
35. [35] M.L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extensions, J. Appl. Mech., 19 (1952), pp. 526-528.