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Transactions of the American Mathematical Society

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Index formulas for elliptic boundary value problems in plane domains with corners

Author: Gregory Eskin
Journal: Trans. Amer. Math. Soc. 314 (1989), 283-348
MSC: Primary 35J40; Secondary 47A53, 58G10
MathSciNet review: 961621
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Abstract: We derive the conditions for the operator corresponding to a general elliptic boundary value problem in a plane domain with corners to be Fredholm and give an explicit formula for the index of this operator.

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  • [1] H. O. Cordes, Pseudo-differential operators on a half-line, J. Math. Mech. 18 (1968/69), 893–908. MR 0435935
  • [2] M. Dauge, Régularités et singularités des solutions de problèmes aux limites elliptiques sur des domains singuliers de type à coins, Thèse, Université de Nantes, 1986.
  • [3] G. I. Eskin, Boundary value problems for elliptic pseudodifferential equations, Translations of Mathematical Monographs, vol. 52, American Mathematical Society, Providence, R.I., 1981. Translated from the Russian by S. Smith. MR 623608
  • [4] -, The conjugacy problem for equations of principal type with two independent variables, Trans. Moscow Math. Soc. 21 (1970), 263-316.
  • [5] G. Eskin, Boundary value problems for second-order elliptic equations in domains with corners, Pseudodifferential operators and applications (Notre Dame, Ind., 1984), Proc. Sympos. Pure Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 105–131. MR 812286, 10.1090/pspum/043/812286
  • [6] P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol. 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 775683
  • [7] V. A. Kondrat′ev and O. A. Oleĭnik, Boundary value problems for partial differential equations in nonsmooth domains, Uspekhi Mat. Nauk 38 (1983), no. 2(230), 3–76 (Russian). MR 695471
  • [8] V. G. Maz'ya and B. A. Plamenevskii, Weighted spaces with nonhomogeneous norms and boundary value problems in domains with conical points, Amer. Math. Soc. Transl. (2) 123 (1984), 89-107.
  • [9] R. B. Melrose and G. Mendoza, Elliptic operators of totally characteristic type, MSRI preprint (1983).
  • [10] K. T. Smith, Formulas to represent functions by their derivatives, Math. Ann. 188 (1970), 53–77. MR 0282046

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Article copyright: © Copyright 1989 American Mathematical Society