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

Fabes, Eugene B.; Garofalo, Nicola

doi:10.1090/S0002-9939-1985-0796447-6

Parabolic B.M.O. and Harnack’s inequality
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by Eugene B. Fabes and Nicola Garofalo PDF

Proc. Amer. Math. Soc. 95 (1985), 63-69 Request permission

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.

References

R. Hanks, Interpolation by the real method between BMO, $L^{\alpha }(0<\alpha <\infty )$ and $H^{\alpha }(0<\alpha <\infty )$, Indiana Univ. Math. J. 26 (1977), no. 4, 679–689. MR 448052, DOI 10.1512/iumj.1977.26.26054

Note on the differentiability of multiple integrals

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F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
Jürgen Moser, On Harnack’s theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577–591. MR 159138, DOI 10.1002/cpa.3160140329
Jürgen Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101–134. MR 159139, DOI 10.1002/cpa.3160170106
J. Moser, On a pointwise estimate for parabolic differential equations, Comm. Pure Appl. Math. 24 (1971), 727–740. MR 288405, DOI 10.1002/cpa.3160240507
Umberto Neri, Some properties of functions with bounded mean oscillation, Studia Math. 61 (1977), no. 1, 63–75. MR 445210, DOI 10.4064/sm-61-1-63-75