| Abstract: |
| Mean value formulas for classical solutions to degenerate linear second order equations in divergence form have been proved in a study in collaboration with Diego Pallara. These results heavily rely on the De Giorgi`s perimeters theory and on its extension to Carnot groups. Based on the classical PDEs theory and on the above mentioned mean value formulas, strong maximum principle and Harnack inequality for classical solutions to stationary subelliptic partial differential equations on Carnot groups have been recently proved by Giulio Pecorella in {\it Fundamental solution, maximum principle and Harnack inequality for second order subelliptic operators} (to appear on Journal of Elliptic and Parabolic Equations). Analogous results have been proved by Annalaura Rebucci in {\it Harnack inequality and maximum principle for degenerate Kolmogorov operators in divergence form} JMAA 128371 (2024) for degenerate Kolmogorov equations. In this seminar we give an overview of the state of research on this subject. |
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