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Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S11
Number of page(s) 27
Published online 01 March 2021
  1. L. Ambrosio, Fine properties of sets of finite perimeter in doubling metric measure spaces. Set-Valued Anal. 10 (2002) 111–128. [Google Scholar]
  2. L. Ambrosio, G. De Philippis and L. Martinazzi, Gamma-convergence of nonlocal perimeter functionals. Manuscripta Math. 134 (2011) 377–403. [Google Scholar]
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  4. L. Ambrosio, B. Kleiner and E. Le Donne Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane. J. Geom. Anal. 19 (2009) 509–540. [Google Scholar]
  5. J. Berendsen and V. Pagliari, On the asymptotic behaviour of nonlocal perimeters. ESAIM: COCV 25 (2019) 48. [EDP Sciences] [Google Scholar]
  6. A. Bonfiglioli, E. Lanconelli and F. Uguzzoni, Stratified Lie Groups and Potential Theory for Their Sub-Laplacians. Springer Monographs in Mathematics. Springer, Berlin (2007). [Google Scholar]
  7. A. Braides, Γ-convergence for Beginners, Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002). [Google Scholar]
  8. X. Cabré, Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory. Ann. Mater. Pura Appl. (2020) 1–17. [Google Scholar]
  9. L. Caffarelli, J.-M. Roquejoffre and O. Savin, Nonlocal minimal surfaces. Commun. Pure Appl. Math. 63 (2010) 1111–1144. [Google Scholar]
  10. L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian. Commun. Partial Diff. Equ. 32 (2007) 1245–1260. [Google Scholar]
  11. L. Capogna, D. Danielli, S.D. Pauls and J.T. Tyson, An Introduction to the Heisenberg Group and the sub-Riemannian Isoperimetric Problem, Vol. 259 of Progress in Mathematics. Birkhäuser Verlag, Basel (2007). [Google Scholar]
  12. E. Cinti, J. Serra and E. Valdinoci, Quantitative flatness results and BV -estimates for stablenonlocal minimal surfaces. J. Diff. Geom. 112 (2019) 447–504. [Google Scholar]
  13. G. Citti, M. Manfredini and A. Sarti, Neuronal oscillations in the visual cortex: Γ-convergence to the Riemannian Mumford-Shah functional. SIAM J. Math. Anal. 35 (2004) 1394–1419. [Google Scholar]
  14. J. Dávila, On an open question about functions of bounded variation. Calc. Var. Partial Diff. Equ. 15 (2002) 519–527. [Google Scholar]
  15. E. De Giorgi Nuovi teoremi relativi alle misure (r − 1)-dimensionali in uno spazio ad r dimensioni. Ricerche Mater. 4 (1955) 95–113. [Google Scholar]
  16. E. De Giorgi and G. Dal Maso Γ-convergence and calculus of variations, in Mathematical Theories of Optimization (Genova, 1981), Vol. 979 of Lecture Notes in Mathematics. Springer, Berlin (1983) 121–143. [Google Scholar]
  17. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  18. S. Dipierro, A comparison between the nonlocal and the classical worlds: minimal surfaces, phase transitions, and geometric flows. Preprint available at (2020). [Google Scholar]
  19. S. Dipierro, A. Figalli, G. Palatucci and E. Valdinoci, Asymptotics of the s-perimeter as s ↘ 0. Discrete Contin. Dyn. Syst. 33 (2013) 2777–2790 (2019). [Google Scholar]
  20. S. Don, E. Le Donne, T. Moisala and D. Vittone, A rectifiability result for finite-perimeter sets in Carnot groups. Preprint available at (2019). [Google Scholar]
  21. S. Don and D. Vittone, Fine properties of functions with bounded variation in Carnot-Carathéodory spaces. J. Math. Anal. Appl. 479 (2019) 482–530. [Google Scholar]
  22. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Textbooks in Mathematics. CRC Press, Boca Raton, FL (2015). [Google Scholar]
  23. H. Federer, Geometric Measure Theory. In Vol. 153 of Die Grundlehren der mathematischen Wissenschafte. Springer-Verlag New York Inc., New York (1969). [Google Scholar]
  24. F. Ferrari and B. Franchi, Harnack inequality for fractional sub-Laplacians in Carnot groups. Math. Z. 279 (2015) 435–458. [Google Scholar]
  25. F. Ferrari, M. Miranda Jr. D. Pallara, A. Pinamonti and Y. Sire, Fractional Laplacians, perimeters and heat semigroups in Carnot groups. Discrete Contin. Dyn. Syst. Ser. S 11 (2018) 477–491. [Google Scholar]
  26. G.B. Folland, A fundamental solution for a subelliptic operator. Bull. Am. Math. Soc. 79 (1973) 373–376. [Google Scholar]
  27. G.B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups. Ark. Mater. 13 (1975) 161–207. [Google Scholar]
  28. 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]
  29. B. Franchi, R. Serapioni and F. Serra Cassano Rectifiabiliy and perimeter in the Heisenberg group. Math. Ann. 321 (2001) 479–531. [Google Scholar]
  30. B. Franchi, R. Serapioni and F. Serra Cassano On the structure of finite perimeter sets in step 2 Carnot groups. J. Geom. Anal. 13 (2003) 421–466. [Google Scholar]
  31. N. Garofalo, Some properties of sub-Laplacians. Electron. J. Diff. Equ. 25 (2018) 103–131. [Google Scholar]
  32. N. Garofalo and D.-M. Nhieu, Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces. Commun. Pure Appl. Math. 49 (1996) 1081–1144. [Google Scholar]
  33. N. Garofalo and G. Tralli, A Bourgain-Brezis-Mironescu-Dávila theorem in Carnot groups of step two. Preprint available at (2020). [Google Scholar]
  34. P. Hajłasz and P. Koskela, Sobolev met Poincaré. Mem. Am. Math. Soc. 145 (2000) 101. [Google Scholar]
  35. E. Le Donne A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries. Anal. Geom. Metr. Spaces 5 (2017) 116–137. [Google Scholar]
  36. E. Le Donne and T. Moisala, Semigenerated step-3 Carnot algebras and applications to sub-Riemannian perimeter. Preprint available at (2020). [Google Scholar]
  37. L. Lombardini, Fractional perimeters from a fractal perspective. Adv. Nonlinear Stud. 19 (2019) 165–196. [Google Scholar]
  38. A. Maalaoui and A. Pinamonti, Interpolations and fractional Sobolev spaces in Carnot groups. Nonlinear Anal. 179 (2019) 91–104. [Google Scholar]
  39. A. Maione, A. Pinamonti and F. Serra Cassano, Γ-convergence for functionals depending on vector fields. II. Convergence of minimizers. Forthcoming. [Google Scholar]
  40. A. Maione, A. Pinamonti and F. Serra Cassano Γ-convergence for functionals depending on vector fields. I. Integral representation and compactness. J. Math. Pure Appl. 139 (2020) 109–142. [Google Scholar]
  41. M. Marchi, Regularity of sets with constant intrinsic normal in a class of Carnot groups. Ann. Inst. Fourier (Grenoble) 64 (2014) 429–455. [Google Scholar]
  42. J.M. Mazón, J.D. Rossi and J. Toledo, Nonlocal perimeter, curvature and minimal surfaces for measurable sets. J. Anal. Math. 138 (2019) 235–279. [Google Scholar]
  43. J. M. Mazón, J.D. Rossi and J.J. Toledo, Nonlocal Perimeter Curvature and Minimal Surfaces for Measurable sets. Frontiers in Mathematics. Birkhäuser/Springer, Cham (2019). [Google Scholar]
  44. J. Mitchell, On Carnot-Carathéodory metrics. J. Diff. Geom. 21 (1985) 35–45. [Google Scholar]
  45. R. Monti, Distances, Boundaries and Surface Measures in Carnot-Carathéodory Spaces. Ph.D.thesis (2001). Available at [Google Scholar]
  46. V. Pagliari, Halfspaces minimise nonlocal perimeter: a proof via calibrations. Ann. Mater. Pure Appl. 199 (2020) 1685–1696. [Google Scholar]
  47. A. Pinamonti, M. Squassina and E. Vecchi, Magnetic BV-functions and the Bourgain-Brezis-Mironescu formula. Adv. Calc. Var. 12 (2019) 225–252. [Google Scholar]
  48. A. Sánchez-Calle, Fundamental solutions and geometry of the sum of squares of vector fields. Invent. Math. 78 (1984) 143–160. [Google Scholar]
  49. O. Savin and E. Valdinoci, Γ-convergence for nonlocal phase transitions. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012) 479–500. [Google Scholar]
  50. E.M. Stein and R. Shakarchi, Complex Analysis, Vol. 2 of Princeton Lectures in Analysis. Princeton University Press, Princeton, NJ (2003). [Google Scholar]
  51. E. Valdinoci, A fractional framework for perimeters and phase transitions. Milan J. Math. 81 (2013) 1–23. [Google Scholar]
  52. V.S. Varadarajan, Lie groups, Lie Algebras, and their Representations. Reprint of the 1974 edition. Vol. 102 of Graduate Texts in Mathematics. Springer-Verlag, New York (1984). [Google Scholar]
  53. N.T. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and Geometry on Groups, Vol. 100 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge (1992). [Google Scholar]
  54. A. Visintin, Nonconvex functionals related to multiphase systems. SIAM J. Math. Anal. 21 (1990) 1281–1304. [Google Scholar]
  55. A. Visintin, Generalized coarea formula and fractal sets. Jpn. J. Ind. Appl. Math. 8 (1991) 175–201. [Google Scholar]

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