Open Access
Issue |
ESAIM: COCV
Volume 31, 2025
|
|
---|---|---|
Article Number | 50 | |
Number of page(s) | 30 | |
DOI | https://doi.org/10.1051/cocv/2025003 | |
Published online | 24 June 2025 |
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. Oxford University Press, Oxford (2000). [Google Scholar]
- L.C. Evans and R.F. Gariepy, Measure Theory and fine Properties of Functions, 2nd revised edn. Textbooks in Mathematics. CRC Press, Boca Raton, FL (2015). [Google Scholar]
- E. De Giorgi, Frontiere orientate di misura minima, Seminario di Matematica della Scuola Normale Superiore di Pisa, 1960-61. Editrice Tecnico Scientifica, Pisa (1961). [Google Scholar]
- E. De Giorgi, Su una teoria generale della misura (r — 1)-dimensionale in uno spazio ad r Dimensioni. Ann. Mat. Pura Appl. Ser. Q. 36 (1954) 191β213. [CrossRef] [Google Scholar]
- E. De Giorgi, Nuovi teoremi relativi alle misure (r — 1)-dimensionali in uno spazio ad r Dimensioni. Ricerche Mat. 4 (1955) 95β113 (in Italian). [MathSciNet] [Google Scholar]
- E. De Giorgi, Sulla proprieta isoperimentrica dell'ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita, Atti della Accademia Nazionale dei Lincei. Memorie. Classe di Scienze Fisiche, Matematiche e Naturali. Serie VIII. Sezione I (Mat. Mec. Astron. Geod. Geofis.) 5 (1958) 33β44 (in Italian). [Google Scholar]
- H. Federer, A note on the Gauss-Green theorem. Proc. Am. Math. Soc. 9 (1958) 447β451. [CrossRef] [Google Scholar]
- H. Federer, Geometric Measure Theory. Grundlehren Math. Wiss., vol. 153. Springer, Cham (1969) (in English). [Google Scholar]
- W.H. Fleming and R. Rishel, An integral formula for total gradient variation. Archiv. Math. 11 (1960) 218β222. [CrossRef] [Google Scholar]
- A.I. Vol'pert, The spaces BV and quasilinear equations. Math. USSR Sbornik 2 (1968) 225β267. [Google Scholar]
- R.V. Kohn, New Estimates for Deformations in Terms of Their Strains. Ph.D. Thesis, Princeton University (1979). [Google Scholar]
- L. Ambrosio, A. Coscia and G. Dal Maso, Fine properties of functions with bounded deformation. Arch. Rational Mech. Anal. 139 (1997) 201β238. [CrossRef] [MathSciNet] [Google Scholar]
- F. Gmeineder and B. Raita, Embeddings for A-weakly differentiable functions on domains. J. Funct. Anal. 277 (2019) 33. [Google Scholar]
- K.T. Smith, Inequalities for formally positive integro-differential forms. Bull. Am. Math. Soc. 67 (1961) 368β370. [CrossRef] [Google Scholar]
- K.T. Smith, Formulas to represent functions by their derivatives. Math. Ann. 188 (1970) 53β77. [CrossRef] [MathSciNet] [Google Scholar]
- A. Arroyo-Rabasa, A. Slicing and fine properties for functions with bounded A-variation arXiv preprint arXiv:2009.13513 (2020) 4. [Google Scholar]
- D. Breit, L. Diening and F. Gmeineder, On the trace operator for functions of bounded A-variation. Anal. PDE 13 (2020) 559β594. [CrossRef] [MathSciNet] [Google Scholar]
- F. Gmeineder, B. Raita and J. Van Schaftingen, On limiting trace inequalities for vectorial differential operators. Indiana Univ. Math. J. 70 (2021) 2133β2176. [CrossRef] [MathSciNet] [Google Scholar]
- B. Raita, Critical Lp-differentiability of BVA-maps and canceling operators. Trans. Am. Math. Soc. 372 (2019) 7297β7326. 10.1090/tran/7878.Zbl1429.26019 [CrossRef] [Google Scholar]
- B. Raita and A. Skorobogatova, Continuity and canceling operators of order n on Rn. Calc. Var. Part. Differ. Equ. 59 (2020) 17.10.1007/s00526-020-01739-z. Id/No 85.Zbl 1443.47046 [CrossRef] [Google Scholar]
- D. Ornstein, A non-inequality for differential operators in the L1 norm. Arch. Rational Mech. Anal. 11 (1962) 40β49. [CrossRef] [MathSciNet] [Google Scholar]
- S. Conti, D. Faraco and F. Maggi, A new approach to counterexamples to L1 estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions. Arch. Rational Mech. Anal. 175 (2005) 287β300. [CrossRef] [MathSciNet] [Google Scholar]
- B. Kirchheim and J. Kristensen, Automatic convexity of rank-1 convex functions. Comptes Rendus Math. Acad. Sci. Paris 349 (2011) 407β409. [CrossRef] [Google Scholar]
- G. Alberti, S. Bianchini and G. Crippa, On the Lp-differentiability of certain classes of functions. Rev. Mat. Iberoamericana 30 (2014) 349β367. [CrossRef] [MathSciNet] [Google Scholar]
- L. Ambrosio, A.C. Ponce and R. Rodiac, Critical weak-Lp differentiability of singular integrals. Rev. Mat. Iberoamericana 36 (2020) 2033β2072. [CrossRef] [MathSciNet] [Google Scholar]
- P. Hajlasz, On approximate differentiability of functions with bounded deformation. Manuscr. Math. 91 (1996) 61β72. [CrossRef] [Google Scholar]
- G. Del Nin, Rectifiability of the jump set of locally integrable functions. Ann. Sc. Norm. Super. Pisa. Cl. Sci. 22 (2021) 1233β1240. [MathSciNet] [Google Scholar]
- N. Aronszajn, On coercive integro-differential quadratic forms. Conf. Part. Differ. Equ. Univ. Kansas 14 (1954) 94β106. [Google Scholar]
- L. Diening and F. Gmeineder, Continuity points via Riesz potentials for C-elliptic Operators. Q. J. Mathem. 71 (2020) 1201β1218. [CrossRef] [Google Scholar]
- W.P. Ziemer, Weakly differentiable functions. Sobolev spaces and functions of bounded Variation. Graduate Texts in Mathematics, Vol. 120. Springer, Cham (1989). [CrossRef] [Google Scholar]
- J. Van Schaftingen, Limiting Sobolev inequalities for vector fields and canceling linear differential Operators. J. Eur. Math. Soc. 15 (2013) 877β921. [CrossRef] [MathSciNet] [Google Scholar]
- J. Bourgain and H. Brezis, New estimates for elliptic equations and Hodge type systems. J. Eur. Math. Soc. 9 (2007) 277β315. [CrossRef] [MathSciNet] [Google Scholar]
- D. Preiss, Geometry of measures in Rn: distribution, rectifiability, and densities. Ann. Math. Second Ser. 125 (1987) 537β643. [CrossRef] [Google Scholar]
- P. Mattila, Geometry of sets and measures in Euclidean spaces. Fractals and Rectifiability. Cambridge Studies in Advanced Mathematics, Vol. 44. Cambridge University Press, Cambridge (1995). [Google Scholar]
- H. Federer, Slices and potentials. Indiana Univ. Math. J. 21 (1971) 373β382. [Google Scholar]
- A. Kalamajska, Pointwise multiplicative inequalities and Nirenberg type estimates in weighted Sobolev spaces. Stud. Math. 108 (1994) 275β290. [CrossRef] [Google Scholar]
- A. Arroyo-Rabasa, Characterization of generalized Young measures generated by A-free Measures. Arch. Rational Mech. Anal. 242 (2021) 235β325. [CrossRef] [MathSciNet] [Google Scholar]
- L. Smith, Nonsingular bilinear forms, generalized J homomorphisms, and the homotopy of spheres. I. Indiana Univ. Math. J. 27 (1978) 697β737. [CrossRef] [Google Scholar]
- P.-M. Suquet, Existence et rΓ©gularite des solutions des equations de la plasticite. Comptes Rendus Hebdomadaires Seances Acad. Sci. Ser. A 286 (1978) 1201β1204 (in French). [Google Scholar]
- R. Temam and G. Strang, Functions of bounded deformation. Arch. Rational Mech. Anal. 75 (1980) 7β21. [Google Scholar]
- Yu. G. Reshetnyak, Estimates for certain differential operators with finite-dimensional kernel. Siberian Math. J. 11 (1970) 315β326. [CrossRef] [Google Scholar]
- A. Arroyo-Rabasa, An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint. Proc. Am. Math. Soc. 148 (2020) 273β282. [Google Scholar]
- A. Arroyo-Rabasa, G. De Philippis, J. Hirsch and F. Rindler, Dimensional estimates and rectifiability for measures satisfying linear PDE constraints. Geom. Funct. Anal. 29 (2019) 639β658. [CrossRef] [MathSciNet] [Google Scholar]
- J. Van Schaftingen, Estimates for L1 -vector fields. Comptes Rendus Math. Acad. Sci. Paris 339 (2004) 181β186. [CrossRef] [MathSciNet] [Google Scholar]
- J. Van Schaftingen, Estimates for L1-vector fields under higher-order differential conditions. J. Eur. Math. Soc. 10 (2008) 867β882. [CrossRef] [MathSciNet] [Google Scholar]
- J. Bourgain and H. Brezis, New estimates for the Laplacian, the div-curl, and related Hodge systems. Comptes Rendus Math. Acad. Sci. Paris 338 (2004) 539β543. [CrossRef] [MathSciNet] [Google Scholar]
- F. Gmeineder, B. Raita and J. Van Schaftingen, Boundary ellipticity and limiting L1-estimates on halfspaces. Adv. Math. 439 (2024) 25. [Google Scholar]
- I. Fonseca and S. Muller, A-quasiconvexity, lower semicontinuity, and Young Measures. SIAM J. Math. [Google Scholar]
- Arroyo-Rabasa, A., De Philippis, G., Hirsch, J., Rindler, F., and Skorobogatova, A. Higher integrability for measures satisfying a PDE constraint. Transactions of the American Mathematical Society, 377, 6195β6224. [Google Scholar]
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