Issue |
ESAIM: COCV
Volume 29, 2023
|
|
---|---|---|
Article Number | 8 | |
Number of page(s) | 21 | |
DOI | https://doi.org/10.1051/cocv/2022084 | |
Published online | 19 January 2023 |
G-convergence of elliptic and parabolic operators depending on vector fields*
1
Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg,
Hermann-Herder-Strasse 10,
79104
Freiburg i. Br.,
Germany
2
Dipartimento di Matematica “Tullio Levi Civita”, Università di Padova,
via Trieste 63,
35121
Padova,
Italy
3
Dipartimento di Matematica, Università di Bologna,
Piazza di Porta San Donato 5,
40126
Bologna,
Italy
** Corresponding author: alberto.maione@mathematik.uni-freiburg.de
Received:
5
May
2022
Accepted:
1
December
2022
We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence, or H-convergence, by means of the compensated compactness theory, in a setting in which the existence of affine functions is not always guaranteed, due to the nature of the family of vector fields.
Mathematics Subject Classification: 35B40 / 35J60 / 35K61 / 35R03 / 47H05 / 53C17
Key words: G-convergence for elliptic and parabolic operators / Nonlinear elliptic equations / Nonlinear parabolic equations / operators depending on vector fields
A. Maione is supported by the DFG SPP 2256 project “Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials” and by the University of Freiburg. A. Maione and F. Paronetto are supported by the INdAM-GNAMPA Project “Equazioni differenziali alle derivate parziali in fenomeni non lineari”. E. Vecchi is supported by INdAM-GNAMPA Project “PDE ellittiche a diffusione mista” (INdAM-GNAMPA Projects Grant number CUP_E55F22000270001).
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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