N. N

Prof. Dr. Jonas Hirsch (Universität Leipzig): On the De Giorgi - Nash - Moser theorem for hypoelliptic operators (joint work with H. Dietert). Kolloquium Partial Differential Equations

Tuesday, 16.05.2023 14:15 im Raum SRZ 203

Mathematik und Informatik

I would like to present a relative simple approach to show uniform boundedness and a weak Harnack inequality for general hypoelliptic operators where ? ? a_{ij} ? ? is uniformly elliptic but merely measurable and the X_i are given smooth vectorfields. Furthermore we assume that they satisfy the Hörmander condition i.e. their Lie-Algebra spans R^{n+1}. The novelty is the avoidance of a "general" Sobolev embedding and a "quantitative" Poincare inequality. Somehow our approach shows that one can somehow consider even the classical De Giorgi-Nash-Moser theorem as a "perturbation" of the poisson equation. If time permits I would like to discuss as well how the geometry of the hypoelliptic equations come into play to obtain as a consequence the famous Hölder regularity.

Prof. Dr. Jonas Hirsch - Title & Abstract.pdf

Angelegt am 06.03.2023 von N. N
Geändert am 08.05.2023 von N. N
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