Scale invariant regularity estimates for second order elliptic equations with lower order coefficients in optimal spaces
Sakellaris, Georgios (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2021
Abstract:	We show local and global scale invariant regularity estimates for subsolutions and supersolutions to the equation -div(A∇u+bu)+c∇u+du=-divf+g, assuming that A is elliptic and bounded. In the setting of Lorentz spaces, under the assumptions b,f∈L, [Formula presented] and c∈L for q≤∞, we show that, with the surprising exception of the reverse Moser estimate, scale invariant estimates with "good" constants (that is, depending only on the norms of the coefficients) do not hold in general. On the other hand, assuming a necessary smallness condition on b,d or c,d, we show a maximum principle and Moser's estimate for subsolutions with "good" constants. We also show the reverse Moser estimate for nonnegative supersolutions with "good" constants, under no smallness assumptions when q<∞, leading to the Harnack inequality for nonnegative solutions and local continuity of solutions. Finally, we show that, in the setting of Lorentz spaces, our assumptions are the sharp ones to guarantee these estimates.
Grants:	European Commission 665919 Ministerio de Ciencia e Innovación MTM-2016-77635-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-395
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Maximum principle ; Moser estimate ; Harnack inequality ; Continuity of solutions ; Lorentz spaces ; Symmetrization
Published in:	Journal de mathématiques pures et appliquées, Vol. 156 (December 2021) , p. 179-214, ISSN 0021-7824

DOI: 10.1016/j.matpur.2021.10.009

36 p, 677.5 KB

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