Parabolic B.M.O. and Harnack's inequality

Authors:
Eugene B. Fabes and Nicola Garofalo

Journal:
Proc. Amer. Math. Soc. **95** (1985), 63-69

MSC:
Primary 35K10; Secondary 35B45

MathSciNet review:
796447

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present a simplified proof of Moser's parabolic version of the lemma of John and Nirenberg. This lemma is used to prove Harnack's inequality for parabolic equations.

**[H]**R. Hanks,*Interpolation by the real method between BMO, 𝐿^{𝛼}(0<𝛼<∞) and 𝐻^{𝛼}(0<𝛼<∞)*, Indiana Univ. Math. J.**26**(1977), no. 4, 679–689. MR**0448052****[JMZ]**B. Jessen, J. Marcinckiewicz and A. Zygmund,*Note on the differentiability of multiple integrals*, Fund. Math.**25**(1935), 217-234.**[JN]**F. John and L. Nirenberg,*On functions of bounded mean oscillation*, Comm. Pure Appl. Math.**14**(1961), 415–426. MR**0131498****[M]**Jürgen Moser,*On Harnack’s theorem for elliptic differential equations*, Comm. Pure Appl. Math.**14**(1961), 577–591. MR**0159138****[M]**Jürgen Moser,*A Harnack inequality for parabolic differential equations*, Comm. Pure Appl. Math.**17**(1964), 101–134. MR**0159139****[M]**J. Moser,*On a pointwise estimate for parabolic differential equations*, Comm. Pure Appl. Math.**24**(1971), 727–740. MR**0288405****[N]**Umberto Neri,*Some properties of functions with bounded mean oscillation*, Studia Math.**61**(1977), no. 1, 63–75. MR**0445210**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
35K10,
35B45

Retrieve articles in all journals with MSC: 35K10, 35B45

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0796447-6

Keywords:
Parabolic equations,
parabolic B.M.O.,
Harnack's inequality

Article copyright:
© Copyright 1985
American Mathematical Society