I am interested in Holder regularity for equations of the form
$$u\_t - div A(x,t) \nabla u = 0$$ where $A(x,t)$ is bounded, measurable and elliptic. 


This was proved in the seminal paper of John Nash and later on by J. Moser.


I am looking for references where Ennio De Giorgi's methods are implemented to obtain the same regularity estimates.



Reference for De Giorgi-Nash-Moser theory
The proof of Harnack's inequality using De Giorgi method has a great flexibility and it can be exteneded even to doubling metric measure spaces that support Poincaré inequalities. 


The elliptic case has been treated in:


J. Kinnunen, N. Shanmugalingam, [Regularity of quasi-minimizers on metric spaces](https://link.springer.com/article/10.1007%2Fs002290100193). *Manuscripta Math.* 105 (2001), 401–423.
([MathScNet review](https://mathscinet.ams.org/mathscinet-getitem?mr=1856619).)


The parabolic case has been treated in:


J. Kinnunen, N. Marola, M. Miranda, Jr., F. Paronetto,
[Harnack's inequality for parabolic De Giorgi classes in metric spaces](https://arxiv.org/abs/1106.5356).
*Adv. Differential Equations* 17 (2012), 801–832. 
([MathScNet review](https://mathscinet.ams.org/mathscinet/search/publdoc.html?pg1=INDI&s1=349676&sort=Newest&vfpref=html&r=25&mx-pid=2985675).)


There are many other related results. Just search references and citations of these two paper in MathSciNet.


