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Proceedings of the American Mathematical Society

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Laplacians and Sobolev Gradients

Author: J. W. Neuberger
Journal: Proc. Amer. Math. Soc. 126 (1998), 2053-2060
MSC (1991): Primary 35A15; Secondary 47F05
MathSciNet review: 1443847
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Abstract: We describe a class of operators which fit the description of laplacians and which may be used to unify the construction of various Sobolev gradients.

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

  • 1. R. A. Adams, Sobolev Spaces, Academic Press, 1978. MR 56:9247
  • 2. A. Beurling and J. Deny, Dirichlet Spaces, Proceedings Nat. Acad. Sci. 45 (1959), 208-215. MR 21:5098
  • 3. A. Beurling, Collected Works, Vol. 2, Editors: L. Carleson, P. Malliavin, J. Neuberger, J. Wermer, Birkhauser, 1989. MR 92k:01046b
  • 4. H. Brezis, Analyse Fonctionnelle, Masson, 1993. MR 85a:46001
  • 5. P. D. Lax, Parabolic Equations, Annls. Math. Stud. V, 167-190. MR 16:709b
  • 6. J. W. Neuberger, Sobolev Gradients and Differential Equations, Lecture Notes in Mathematics #1670, Springer, 1997.
  • 7. F. Riesz and B. Sz.-Nagy, Functional Analysis, Ungar, 1955. MR 17:175i
  • 8. J. VonNeumann, Functional Operators II, Annls. Math. Stud. 22, 1950. MR 11:599e
  • 9. H. Weyl, The method of orthogonal projections in potential theory, Duke Math.J. 7 (1940), 411-444. MR 2:202a

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Additional Information

J. W. Neuberger
Affiliation: Department of Mathematics, University of North Texas, Denton, Texas 76203

Keywords: Laplacian, Sobolev gradient
Received by editor(s): March 15, 1996
Received by editor(s) in revised form: December 18, 1996
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1998 American Mathematical Society