Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] H. O. Cordes, Pseudodifferential operators on a half-line, J. Math. Mech. 18 (1968/69), 893-908. MR 0435935 (55:8886)
  • [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, Transl. Math. Monographs, vol. 52, Amer. Math. Soc., Providence, R.I., 1981. MR 623608 (82k:35105)
  • [4] -, The conjugacy problem for equations of principal type with two independent variables, Trans. Moscow Math. Soc. 21 (1970), 263-316.
  • [5] -, Boundary value problems for second order elliptic equations in domains with corners, Proc. Sympos. Pure Math., vol. 43, Amer. Math. Soc., Providence, R.I., 1985, pp. 105-131. MR 812286 (87e:35028)
  • [6] P. Grisvard, Elliptic problems in nonsmooth domains, Pitman, London, 1985. MR 775683 (86m:35044)
  • [7] V. A. Kondrat'ev and O. A. Oleinik, Boundary value problems for partial differential equations in nonsmooth domains, Russian Math. Surveys 38 (1983), 1-86. MR 695471 (85j:35002)
  • [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 (43:7760)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35J40, 47A53, 58G10

Retrieve articles in all journals with MSC: 35J40, 47A53, 58G10

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society