From: rusin@math.niu.edu (Dave Rusin)
Subject: Re: Teorema De Giorgi - Nash.
Date: 29 Apr 1999 15:04:31 GMT
Newsgroups: sci.math.research

Tiberio Marzano <tiberiox@tin.it> wrote:
>Cerco l'enunciato e dei commenti sul teorema De Giorgi - Nash.

Since no one else has responded, I scanned Math Reviews for a summary.

   88b:35037 35B45 (35K10 58C15) 
   Fabes, E. B.(1-MN); Stroock, D. W.(1-MIT)
   A new proof of Moser's parabolic Harnack inequality using the old
   ideas of Nash.
   Arch. Rational Mech. Anal. 96 (1986), no. 4, 327--338. 
   
   One of the key results in elliptic regularity theory is that weak
   solutions of linear elliptic equations with bounded measurable 
   coefficients are locally Holder-continuous. This result was
   established independently by E. De Giorgi [Mem. Accad. Sci. Torino Cl.
   Sci. Fis. Mat. Natur. (3) 3 (1957), 25--43; MR 20 #172] and J. F.
   Nash, Jr. [Amer. J. Math. 80 (1958), 931--954; MR 20 #6592].
   Subsequently, J. Moser provided a very understandable treatment [Comm.
   Pure Appl. Math. 14 (1961), 577--591; MR 28 #2356].
   [...]

   Reviewed by W. P. Ziemer

   �� Copyright American Mathematical Society 1999