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.

**[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]**-,*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*,*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)**

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