EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 31 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 31
Number of page(s) 33
DOI https://doi.org/10.1051/cocv/2024022
Published online 16 April 2024
  1. J. Björn, S. Buckley and S. Keith, Admissible measures in one dimension. Proc. Amer. Math. Soc. 134 (2005) 703–705. [CrossRef] [Google Scholar]
  2. V.V. Zhikov, On the density of smooth functions in a weighted Sobolev space, (Russian). Dokl. Akad. Nauk 453 (2013) 247–251; translation in Dokl. Math. 88 (2013) 669–673. [Google Scholar]
  3. J. Casado-Díaz, Relaxation of a quadratic functional defined by a nonnegative unbounded matrix. Potential Anal. 11 (1999) 39–76. [CrossRef] [MathSciNet] [Google Scholar]
  4. N. Fusco and G. Moscariello, L2-Lower semicontinuity of functionals of quadratic type. Ann. Mat. Pura Appl. 129 (1981) 305–326. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Marcellini, Some problems of semicontinuity and of Γ-Convergence for integrals of the calculus of variations, in Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, May 8–12, 1978), edited by E. De Giorgi, E. Magenes and U. Mosco. Pitagora, Bologna (1979) 205–221. [Google Scholar]
  6. P. Marcellini and C. Sbordone, An approach to the asymptotic behaviour of ellipltic-parabolic operators. J. Math. Pures Appl. 56 (1977) 157–182. [MathSciNet] [Google Scholar]
  7. F. Acanfora, G. Cardone and S. Mortola, On the variational convergence of non-coercive quadratic integral functionals and semicontinuity problems. NoDEA Nonlinear Differ. Equ. Appl. 10 (2003) 347–373. [CrossRef] [Google Scholar]
  8. J.J. Alibert and P. Seppecher, Closure of the set of diffusion functionals – the one dimensional case. Potential Anal. 28 (2008) 335–356. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Briane, Nonlocal effects in two-dimensional conductivity. Arch. Ration. Mech. Anal. 182 (2006) 255–267. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Camar-Eddine and P. Seppecher, Closure of the set of diffusion functionals with respect to the Mosco-convergence. Math. Models Methods Appl. Sci. 12 (2002) 1153–1176. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Belloni and G. Buttazzo, A survey on old and recent results about the gap phenomenon in the calculus of variations. Recent developments in well-posed variational problems. Math. Appl. 331 (1995) 1–27. [Google Scholar]
  12. U. Mosco, Composite media and asymptotic Dirichlet forms. J. Funct. Anal. 123(2) (1994) 368–421. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Cheeger, Differentiability of Lipschitz functions on metric measure spaces. Geom. Funct. Anal. 9 (1999) 428–517. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Ambrosio, M. Colombo and S. Di Marino, Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope, Variational methods for evolving objects. Adv. Stud. Pure Math. 67 (2015). [CrossRef] [Google Scholar]
  15. L. Ambrosio and R. Ghezzi, Sobolev and bounded variations functions in metric measure spaces, in Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds, Vol. II. EMS Ser. Lect. Math. Eur. Math. Soc., Zurich (2016) 211–273. [CrossRef] [Google Scholar]
  16. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2nd edn. Lectures in Mathematics ETH Zurich. Birkhauser Verlag, Basel (2008). [Google Scholar]
  17. L. Ambrosio, N. Gigli and G. Savaré, Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces. Rev. Mat. Iberoam. 29 (2013) 969–996. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Ambrosio, N. Gigli and G. Savaré, Heat flow and calculus on metric measure spaces with Ricci curvature bounded below – the compact case. Analysis and Numerics of Partial Differential Equations. Springer INdAM Ser., 4, Springer, Milan (2013) 63–115. [CrossRef] [Google Scholar]
  19. L. Ambrosio, N. Gigli and G. Savaré, Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below. Invent. Math. 195 (2014) 289–391. [CrossRef] [MathSciNet] [Google Scholar]
  20. L. Ambrosio, A. Pinamonti and G. Speight, Tensorization of Cheeger energies, the space H1,1 and the area formula for graphs. Adv. Math. 281 (2015) 1145–1177. [CrossRef] [MathSciNet] [Google Scholar]
  21. L. Ambrosio, A. Pinamonti and G. Speight, Weighted Sobolev spaces on metric measure spaces. J. Reine Angew. Math. 746 (2019) 39–65. [CrossRef] [Google Scholar]
  22. J. Heinonen, P. Koskela, N. Shanmugalingam and J. Tyson, Sobolev spaces on metric measure spaces. An approach based on upper gradients. New Mathematical Monographs, 27. Cambridge University Press, Cambridge (2015). [Google Scholar]
  23. B. Opic and A. Kufner, Hardy-type inequalities.. Pitman Research Notes in Mathematics Series (2019). [Google Scholar]
  24. B. Franchi, F. Serra Cassano and R. Serapioni, 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]
  25. F. Serra Cassano, On the local boundedness of certain solutions for a class of degenerate elliptic equations. Boll. Un. Mat. Ital. B 10 (1996) 651–680. [MathSciNet] [Google Scholar]
  26. E. Fabes, C. Kenig and R. Serapioni, The local regularity of solutions of degenerate elliptic equations. Commun. PDE 7 (1982) 77–116. [CrossRef] [Google Scholar]
  27. V. Chiadió Piat and F. Serra Cassano, Some remarks about the density of smooth functions in weighted Sobolev spaces. J. Convex Anal. 1 (1994) 135–142. [MathSciNet] [Google Scholar]
  28. M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland Math. Library, 23. North-Holland & Kodansha. Amsterdam (1980). [Google Scholar]
  29. M. Biroli, U. Mosco, A Saint-Venant principle for Dirichlet forms on discontinuous media. Ann. Mat. Pura Appl. 169 (1995) 125–181. [CrossRef] [MathSciNet] [Google Scholar]
  30. M.M. Hamza, Determination des formes de Dirichlet sur ℝn, Thèse 3-eme cycle. Université d’Orsay (1975). [Google Scholar]
  31. D.L. Cohn, Measure Theory. Birkhäuser (1980). [CrossRef] [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.