We review local regularity properties of the non-cutoff Boltzmann equation for moderately soft potentials. We explain how to view the Boltzmann equation as a non-local hypoelliptic equation. We show that despite its non-locality, we can derive a Strong Harnack inequality. To this end, we establish a linear First De Giorgi Lemma, which relates the local supremum to the local norm without non-local tail terms.
@article{SLSEDP_2023-2024____A1_0, author = {Am\'elie Loher}, title = {Strong {Harnack} inequality for the {Boltzmann} equation}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:1}, pages = {1--15}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2023-2024}, doi = {10.5802/slsedp.164}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.164/} }
TY - JOUR AU - Amélie Loher TI - Strong Harnack inequality for the Boltzmann equation JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:1 PY - 2023-2024 SP - 1 EP - 15 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.164/ DO - 10.5802/slsedp.164 LA - en ID - SLSEDP_2023-2024____A1_0 ER -
%0 Journal Article %A Amélie Loher %T Strong Harnack inequality for the Boltzmann equation %J Séminaire Laurent Schwartz — EDP et applications %Z talk:1 %D 2023-2024 %P 1-15 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.164/ %R 10.5802/slsedp.164 %G en %F SLSEDP_2023-2024____A1_0
Amélie Loher. Strong Harnack inequality for the Boltzmann equation. Séminaire Laurent Schwartz — EDP et applications (2023-2024), Exposé no. 1, 15 p. doi : 10.5802/slsedp.164. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.164/
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