Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Isotopic families of contact manifolds for elliptic PDE

Authors: Mark L. Agranovsky and E. K. Narayanan
Journal: Proc. Amer. Math. Soc. 134 (2006), 2117-2123
MSC (2000): Primary 35J67; Secondary 35B60
Published electronically: January 17, 2006
MathSciNet review: 2215782
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A test for a function to be a solution of an elliptic PDE is given in terms of extensions, as solutions, from the boundaries inside the domains belonging to an isotopic family. It generalizes a result of Ehrenpreis for spheres moved along a straight line.

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

  • 1. M. L. Agranovsky and R. E. Val'sky, Maximality of invariant algebras of functions, Siberian Math.J. 12 (1971), 1-7.
  • 2. M.L. Agranovsky and J.Globevnik, Analyticity on circles for rational and real-analytic functions of two real variables, J. Analyse Math. 91 (2003), 31-65. MR 2037401 (2004j:30003)
  • 3. L.Ehrenpreis, Three problems at Mount Holyoke, Contemp. Math. 278 (2001), 123-130. MR 1851483 (2002d:44002)
  • 4. L. Ehrenpreis, The Universality of the Radon Transform, Oxford Univ. Press,2003. MR 2019604
  • 5. J. Globevnik, Analyticity on rotation invariant families of circles, Trans. Amer. Math. Soc. 280 (1983), 247-254. MR 0712259 (85f:30060)
  • 6. J.Globevnik, Testing analyticity on rotation invariant families of curves, Trans. Amer. Math. Soc. 306 (1988), 401-410. MR 0927697 (89g:30078)
  • 7. J. Globevnik Holomorphic extensions and rotation invariance, Complex Variables, 24 (1993), 49-51. MR 1269830 (95g:30002)
  • 8. J. Globevnik, Holomorphic extensions from open families of circles, Trans. Amer. Math. Soc. 355 (2003), 1921-1931. MR 1953532 (2003j:30007)
  • 9. N. N. Tarkhanov, The Cauchy Problem for Solutions of Elliptic Equations, Academie Verlag, Berlin, 1995. MR 1334094 (96d:35024)
  • 10. A.Tumanov,A Morera type theorem in the strip,Math.Res. Lett., 11 (2004), no. 1, 23-29. MR 2046196 (2004k:30004)
  • 11. L. Zalcman,Analyticity and the Pompeiu problem, Arch. Rat. Mech. Anal. 47 (1972), 237-254. MR 0348084 (50:582)
  • 12. L. Zalcman, Offbeat integral geometry, Amer. Math. Monthly, 87 (1980), no.3, 161-175. MR 0562919 (81b:53046)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J67, 35B60

Retrieve articles in all journals with MSC (2000): 35J67, 35B60

Additional Information

Mark L. Agranovsky
Affiliation: Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

E. K. Narayanan
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore - 560 012, India

Keywords: Contact manifolds, Dirichlet-Neumann problem, Green's formula.
Received by editor(s): October 11, 2004
Received by editor(s) in revised form: February 21, 2005
Published electronically: January 17, 2006
Additional Notes: The first author was partially supported by Israel Scientific Foundation, grant No. 279/02-01.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society

American Mathematical Society