Open Access
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
  1. A. Baldi, B. Franchi, N. Tchou and M.C. Tesi, Compensated compactness for differential forms in Carnot groups and applications. Adv. Math. 223 (2010) 1555–1607. [CrossRef] [MathSciNet] [Google Scholar]
  2. V. Chiado Piat, G. Dal Maso and A. Defranceschi, G-convergence of monotone operators. Ann. Inst. H. Poincaré, Anal. Non Linéaire 7 (1990) 123–160. [CrossRef] [MathSciNet] [Google Scholar]
  3. F. Colombini and S. Spagnolo, Sur la convergence de solutions d’equations paraboliques. J. Math. Pures Appl. 56 (1977) 263–305. [MathSciNet] [Google Scholar]
  4. G. Dal Maso, An introduction to T-convergence. Birkhauser, Boston (1993). [Google Scholar]
  5. E. De Giorgi and T. Franzoni, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 58 (1975) 842–850. [MathSciNet] [Google Scholar]
  6. E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell’energia per operatori ellittici del secondo ordine. Boll. Un. Mat. Ital. 8 (1973) 391–411. [MathSciNet] [Google Scholar]
  7. F. Essebei, A. Pinamonti and S. Verzellesi, Integral representation of local functionals depending on vector fields. To appear in Adv. Calc. Var. (2022) https://doi.org/10.1515/acv-2021-0054. [Google Scholar]
  8. F. Essebei and S. Verzellesi, T-compactness of some classes of integral functionals depending on vector fields. Preprint available at https://arxiv.org/pdf/2112.05491.pdf. [Google Scholar]
  9. G.B. Folland and E.M. Stein, Hardy spaces on homogeneous groups. Mathematical Notes 28. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo (1982). [Google Scholar]
  10. B. Franchi, C.E. Gutierrez and T. van Nguyen, Homogenization and convergence of correctors in Carnot groups. Commun. Partial Differ. Equ. 30 (2005) 1817–1841. [CrossRef] [Google Scholar]
  11. B. Franchi, N. Tchou and M.C. Tesi, Div-curl type theorem, H-convergence and Stokes formula in the Heisenberg group. Commun. Contemp. Math. 8 (2006) 67–99. [CrossRef] [Google Scholar]
  12. B. Franchi and M.C. Tesi, Two-scale homogenization in the Heisenberg group. J. Math. Pures Appl. 81 (2002) 495–532. [CrossRef] [MathSciNet] [Google Scholar]
  13. B. Franchi, R. Serapioni and F. Serra Cassano, Meyers-Serrin type theorems and relaxation of variational integrals depending on vector fields. Houston J. Math. 22 (1996) 859–890. [Google Scholar]
  14. B. Franchi, R. Serapioni and F. Serra Cassano, Approximation and imbedding theorems for weighted Sobolev spaces associated with Lipschitz continuous vector fields. Boll. Un. Mat. Ital. B 11 (1997) 83–117. [MathSciNet] [Google Scholar]
  15. N. Garofalo and D.-M. Nhieu, Isoperimetric and Sobolev inequalities for Carnot-Caratheodory spaces and the existence of minimal surfaces. Commun. Pure Appl. Math. 49 (1996) 1081–1144. [CrossRef] [Google Scholar]
  16. A. Maione, H-convergence for equations depending on monotone operators in Carnot groups. Electr. J. Differ. Equ. 2021 (2021) 1–13. [CrossRef] [Google Scholar]
  17. A. Maione, A. Pinamonti and F. Serra Cassano, T-convergence for functionals depending on vector fields. I. Integral representation and compactness. J. Math. Pures Appl. 139 (2020) 109–142. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Maione, A. Pinamonti and F. Serra Cassano, T-convergence for functionals depending on vector fields. II. Convergence of minimizers. SIAM J. Math. Anal. 54 (2022) 5761–5791. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Maione and E. Vecchi, Integral representation of local left-invariant functionals in Carnot groups. Anal. Geom. Metr. Spaces 8 (2020) 1–14. [CrossRef] [MathSciNet] [Google Scholar]
  20. N.G. Meyers and J. Serrin, H = W. Proc. Nat. Acad. Sci. USA 51 (1964) 1055–1056. [CrossRef] [PubMed] [Google Scholar]
  21. M. Francois and T. Luc, H-convergence, Topics in the mathematical modelling of composite materials, Progr. Nonlinear Differential Equations Appl. 31 (1997) 21–43. [Google Scholar]
  22. A. Pankov, G-convergence and homogenization of nonlinear partial differential operators, Mathematics and its Applications 422. Kluwer Academic Publishers, Dordrecht (1997). [Google Scholar]
  23. R.E. Showalter, Monotone operators in Banach space and nonlinear partial differential equations, (English summary) Mathematical Surveys and Monographs, 49. American Mathematical Society, Providence, RI (1997). [Google Scholar]
  24. L. Simon, On G-convergence of elliptic operators. Indiana Univ. Math. J. 28 (1979) 587–594. [CrossRef] [MathSciNet] [Google Scholar]
  25. S. Spagnolo, Convergence of parabolic equations. Boll. Un. Mat. Ital. B 14 (1977) 547–568. [MathSciNet] [Google Scholar]
  26. S. Spagnolo, Una caratterizzazione degli operatori differenziali autoaggiunti del 2° ordine a coefficienti misurabili e limitati. Rend. del Sem,. Mat. dell’Univ. di Padova 39 (1967) 56–64. [Google Scholar]
  27. S. Spagnolo, Sul limite delle soluzioni di problemi di Cauchy relativi all’equazione del calore. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 21 (1967) 657–699. [MathSciNet] [Google Scholar]
  28. S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche. Ann. Scuola Norm. Sup. Pisa 22 (1968) 571–597; errata, ibid. (3) 22, 673. [Google Scholar]
  29. N. Svanstedt, G-convergence of parabolic operators. Nonlinear Anal. 36 (1999) 807–842. [CrossRef] [MathSciNet] [Google Scholar]
  30. L. Tartar, The general theory of homogenization, A personalized introduction. Lecture Notes of the Unione Matematica Italiana 7. Springer-Verlag, Berlin; UMI, Bologna (2009). [Google Scholar]
  31. E. Zeidler, Nonlinear functional analysis and its applications. II/A, II/B. Springer-Verlag, New York (1990). [Google Scholar]
  32. V.V. Zikov, S.M. Kozlov and O.A. Olemik, G-convergence of parabolic operators. Uspekhi Mat. Nauk 36 (1981) 11–58, 248. [MathSciNet] [Google Scholar]
  33. V.V. Zikov, S.M. Kozlov, O.A. Oleïnik and H.T. Ngoan, Averaging and G-convergence of differential operators. Uspekhi Mat. Nauk 34 (1979) 65–133, 256. [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.