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Local Vs Nonlocal De Giorgi Classes: A brief guide in the homogeneous case
Cassanello, Filippo
Ciani, Simone
Majrashi, Bashayer
Vespri, Vincenzo
2025
Abstract
We give a brief and concise guide for the analysis of the local behavior of the elements of local and nonlocal homogeneous De Giorgi classes: local boundedness, local H¨older continuity and Harnacktype inequalities. In the local case, we promote a simplified itinerary in the classic theory, propaedeutic for the successive part; while in the nonlocal case, we gather recent new developments into an unitary and concise framework. Employing a suitable definition of De Giorgi classes, we show a new proof of the Harnack inequality, way easier than in the local case, that bypasses any sort of Krylov-Safonov argument or cube decomposition.
Publisher
EUT Edizioni Università di Trieste
Source
Filippo Cassanello, Simone Ciani, Bashayer Majrashi, and Vincenzo Vespri, "Local Vs Nonlocal De Giorgi Classes: A brief guide in the homogeneous case" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.57 (2025)", EUT Edizioni Università di Trieste, Trieste, 2025, pp.
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
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