Volume 29, 2023
|Number of page(s)||21|
|Published online||19 January 2023|
G-convergence of elliptic and parabolic operators depending on vector fields*
Abteilung für Angewandte Mathematik, Albert-Ludwigs-Universität Freiburg,
Freiburg i. Br.,
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: firstname.lastname@example.org
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
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