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)

 
 

 

A Fatou theorem for solutions of the porous medium equation


Authors: Björn E. J. Dahlberg, Eugene B. Fabes and Carlos E. Kenig
Journal: Proc. Amer. Math. Soc. 91 (1984), 205-212
MSC: Primary 35K55; Secondary 35B40, 76S05
DOI: https://doi.org/10.1090/S0002-9939-1984-0740172-3
MathSciNet review: 740172
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that nonnegative solutions of the porous medium equation in an infinite strip have nontangential initial values pointwise almost everywhere.


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

  • [A] D. G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967), 890-897. MR 0217444 (36:534)
  • [A$ _{2}$] -, Non-negative solutions of linear parabolic equations: an addendum, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1971), 221-228.
  • [AC] D. G. Aronson and L. A. Caffarelli, The initial trace of a solution of the porous medium equation, preprint. MR 712265 (85c:35042)
  • [BCP] P. Benilan, M. Crandall and M. Pierre, Solutions of the porous media equation in $ {R^N}$, under optimal conditions on initial values, Indiana Univ. Math. J. (to appear). MR 726106 (86b:35084)
  • [C] A. P. Calderon, On the behavior of harmonic functions at the boundary, Trans. Amer. Math. Soc. 68 (1950), 47-54. MR 0032863 (11:357e)
  • [DK] B. E. J. Dahlberg and C. E. Kenig, Non-negative solutions of the porous medium equation, in preparation.
  • [S] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1971. MR 0290095 (44:7280)
  • [W] D. Widder, Positive temperature on the infinite rod, Trans. Amer. Math. Soc. 55 (1944), 85-95. MR 0009795 (5:203f)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35K55, 35B40, 76S05

Retrieve articles in all journals with MSC: 35K55, 35B40, 76S05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0740172-3
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society