The proof of Harnack inequality using DeGiorgi method has a great flexibility and it can be exteneded even to doubling metric measure spaces that support Poincare inequalities.

The elliptic case has been treated in:

J. Kinnunen, N. Shanmugalingam, Regularity of quasi-minimizers on metric spaces. Manuscripta Math. 105 (2001), 401–423. (MathScNet review.)

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. Adv. Differential Equations 17 (2012), 801–832. (MathScNet review.)

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

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. Manuscripta Math. 105 (2001), 401–423. (MathScNet review.)

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. Adv. Differential Equations 17 (2012), 801–832. (MathScNet review.)

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

The proof of Harnack inequality using DeGiorgi method has a great flexibility and it can be exteneded even to doubling metric measure spaces that support Poincare inequalities.

The elliptic case has been treated in:

J. Kinnunen, N. Shanmugalingam, Regularity of quasi-minimizers on metric spaces. Manuscripta Math. 105 (2001), 401–423.

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. Adv. Differential Equations 17 (2012), 801–832.

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

The proof of Harnack inequality using DeGiorgi method has a great flexibility and it can be exteneded even to doubling metric measure spaces that support Poincare inequalities.

The elliptic case has been treated in:

J. Kinnunen, N. Shanmugalingam, Regularity of quasi-minimizers on metric spaces. Manuscripta Math. 105 (2001), 401–423. (MathScNet review.)

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. Adv. Differential Equations 17 (2012), 801–832. (MathScNet review.)

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