Le déterminant jacobien [d'après Brezis et Nguyen]
Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Exposé no. 1041, 20 p.
@incollection{AST_2012__348__405_0,
     author = {Mironescu, Petru},
     title = {Le d\'eterminant jacobien [d'apr\`es {Brezis} et {Nguyen]}},
     booktitle = {S\'eminaire Bourbaki Volume 2010/2011 Expos\'es 1027-1042. Avec table par noms d'auteurs de 1948/49 \`a 2009/10.},
     series = {Ast\'erisque},
     note = {talk:1041},
     pages = {405--424},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {348},
     year = {2012},
     zbl = {1277.46018},
     language = {fr},
     url = {http://archive.numdam.org/item/AST_2012__348__405_0/}
}
TY  - CHAP
AU  - Mironescu, Petru
TI  - Le déterminant jacobien [d'après Brezis et Nguyen]
BT  - Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10.
AU  - Collectif
T3  - Astérisque
N1  - talk:1041
PY  - 2012
SP  - 405
EP  - 424
IS  - 348
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2012__348__405_0/
LA  - fr
ID  - AST_2012__348__405_0
ER  - 
%0 Book Section
%A Mironescu, Petru
%T Le déterminant jacobien [d'après Brezis et Nguyen]
%B Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10.
%A Collectif
%S Astérisque
%Z talk:1041
%D 2012
%P 405-424
%N 348
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2012__348__405_0/
%G fr
%F AST_2012__348__405_0
Mironescu, Petru. Le déterminant jacobien [d'après Brezis et Nguyen], dans Séminaire Bourbaki Volume 2010/2011 Exposés 1027-1042. Avec table par noms d'auteurs de 1948/49 à 2009/10., Astérisque, no. 348 (2012), Exposé no. 1041, 20 p. http://archive.numdam.org/item/AST_2012__348__405_0/

[1] L. V. Ahlfors - Zur Theorie der Überlagerungsflächen, Acta Math. 65 (1935), p. 157-194. | DOI | JFM

[2] L. V. Ahlfors, Lectures on quasiconformal mappings, 2e éd., University Lecture Series, vol. 38, Amer. Math. Soc., 2006. | Zbl

[3] G. Alberti, S. Baldo & G. Orlandi - Functions with prescribed singularities, J. Eur. Math. Soc. (JEMS) 5 (2003), p. 275-311. | DOI | EuDML | Zbl

[4] J. M. Ball - Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1976/77), p. 337-403. | DOI | Zbl

[5] J. M. Ball & F. Murat - W 1 , p -quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984), p. 225-253. | DOI | Zbl

[6] C. Bennett - Intermediate spaces and the class L log + L , Ark. Mat. 11 (1973), p. 215-228. | DOI | Zbl

[7] C. Bennett & K. Rudnick - On Lorentz-Zygmund spaces, Dissertationes Math. (Rozprawy Mat.) 175 (1980). | Zbl

[8] J. Bourgain, H. Brezis & P. Mironescu - Complements to the paper « Lifting, degree and the distributional Jacobian revisited », http://math.univ-lyon1.fr/˜mironescu/2.pdf, 2004.

[9] J. Bourgain, H. Brezis & P. Mironescu, H 1 / 2 maps with values into the circle : minimal connections, lifting, and the Ginzburg-Landau equation, Publ. Math. IHÉS 99 (2004), p. 1-115. | DOI | EuDML | Numdam | Zbl

[10] J. Bourgain, H. Brezis & P. Mironescu, Lifting, degree, and distributional Jacobian revisited, Comm. Pure Appl. Math. 58 (2005), p. 529-551. | DOI | Zbl

[11] J. Bourgain, H. Brezis & H.-M. Nguyen - A new estimate for the topological degree, C. R. Math. Acad. Sci. Paris 340 (2005), p. 787-791. | DOI | Zbl

[12] H. Brezis, J.-M. Coron & E. H. Lieb - Harmonic maps with defects, Comm. Math. Phys. 107 (1986), p. 649-705. | DOI | Zbl

[13] H. Brezis, N. Fusco & C. Sbordone - Integrability for the Jacobian of orientation preserving mappings, J. Funct. Anal. 115 (1993), p. 425-431. | DOI | Zbl

[14] H. Brezis & H.-M. Nguyen - The Jacobian determinant revisited, à paraître dans Invent. Math. | Zbl

[15] H. Brezis & H.-M. Nguyen, On the distributional Jacobian of maps from 𝕊 N into 𝕊 N in fractional Sobolev and Hölder spaces, à paraître dans Ann. Math. | Zbl

[16] H. Brezis & L. Nirenberg - Degree theory and BMO. I. Compact manifolds without boundaries, Selecta Math. (N.S.) 1 (1995), p. 197-263. | DOI | Zbl

[17] R. Coifman, P.-L. Lions, Y. Meyer & S. Semmes - Compensated compact-ness and Hardy spaces, J. Math. Pures Appl. 72 (1993), p. 247-286. | Zbl

[18] B. Dacorogna & F. Murat - On the optimality of certain Sobolev exponents for the weak continuity of determinants, J. Funct. Anal. 105 (1992), p. 42-62. | DOI | Zbl

[19] H. Federer - Geometric measure theory, Die Grund. Math. Wiss., Band 153, Springer New York Inc., New York, 1969. | Zbl

[20] C. Fefferman - Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), p. 587-588. | DOI | Zbl

[21] A. Fletcher & V. Markovic - Quasiconformal maps and Teichmüller theory, Oxford Graduate Texts in Math., vol. 11, Oxford Univ. Press, 2007. | Zbl

[22] F. C. Frank - On the theory of liquid crystals, Discuss. Faraday Soc. 25 (1958). | DOI

[23] E. Gagliardo - Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili, Rend. Sem. Mat. Univ. Padova 27 (1957), p. 284-305. | EuDML | Numdam | Zbl

[24] E. Gagliardo, Ulteriori proprietà di alcune classi di funzioni in più variabili, Ricerche Mat. 8 (1959), p. 24-51. | Zbl

[25] P.-G. De Gennes & J. Prost - The physics of liquid crystals, Intern. Series of Monographs in Physics, Oxford Univ. Press, 1993.

[26] H. Grötzsch - Über einige Extremalprobleme der konformen Abbildung. I, II, Berichte Leipzig 80 (1928), p. 367-376, 497-502. | JFM

[27] F. Hang & F. Lin - A remark on the Jacobians, Commun. Contemp. Math. 2 (2000), p. 35-46. | DOI | Zbl

[28] T. Iwaniec - p -harmonic tensors and quasiregular mappings, Ann. of Math. 136 (1992), p. 589-624. | DOI | Zbl

[29] T. Iwaniec, Null Lagrangians, the art of integration by parts, in The interaction of analysis and geometry, Contemp. Math., vol. 424, Amer. Math. Soc., 2007, p. 83-102. | DOI | Zbl

[30] T. Iwaniec & C. Sbordone - On the integrability of the Jacobian under minimal hypotheses, Arch. Rational Mech. Anal. 119 (1992), p. 129-143. | DOI | Zbl

[31] B. Jawerth - Some observations on Besov and Lizorkin-Triebel spaces, Math. Scand. 40 (1977), p. 94-104. | DOI | EuDML | Zbl

[32] F. John - Rotation and strain, Comm. Pure Appl. Math. 14 (1961), p. 391-413. | DOI | Zbl

[33] F. John & L. Nirenberg - On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), p. 415-426. | DOI | Zbl

[34] A. Korn - Solution générale du problème d'équilibre dans la théorie de l'élasticité, dans le cas où les efforts sont donnés à la surface, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 10 (1908), p. 165-269. | EuDML | JFM | Numdam

[35] A. Korn, Über einige Ungleichungen, welche in der Theorie der elastischen und elektrischen Schwingungen eine Rolle spielen, Bulletin International, Cracovie Akademie Umiejet, Classe des sciences mathématiques et naturelles (1909), p. 705-724. | JFM

[36] M. A. Lavrent'Ev - Sur une classe de représentations continues, Mat. Sb. 42 (1935), p. 407-424. | EuDML | JFM | Zbl

[37] M. A. Lavrent'Ev, Sur un critère différentiel des transformations homéomorphes des domaines à trois dimensions, Dokl. Akad. Nauk SSSR 20 (1938), p. 241-242. | JFM | Zbl

[38] J. Mawhin - Communication personnelle.

[39] P. Mironescu - Sobolev maps on manifolds : degree, approximation, lifting, in Perspectives in nonlinear partial differential equations, Contemp. Math., vol. 446, Amer. Math. Soc., 2007, p. 413-436. | DOI | Zbl

[40] P. Mironescu & W. Sickel - En préparation.

[41] A. Boutet De Monvel-Berthier, V. Georgescu & R. Purice - A boundary value problem related to the Ginzburg-Landau model, Comm. Math. Phys. 142 (1991), p. 1-23. | DOI | MR | Zbl

[42] C. B. Morrey, Jr. - Multiple integrals in the calculus of variations, Grundl. Math. Wiss., vol. 130, Springer New York, Inc., New York, 1966. | MR | Zbl

[43] S. Müller - Higher integrability of determinants and weak convergence in L 1 , J. reine angew. Math. 412 (1990), p. 20-34. | EuDML | MR | Zbl

[44] F. Murat - Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5 (1978), p. 489-507. | EuDML | Numdam | MR | Zbl

[45] F. Murat, Compacité par compensation. II, in Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), Pitagora, 1979, p. 245-256. | MR | Zbl

[46] F. Murat, Compacité par compensation : condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8 (1981), p. 69-102. | EuDML | Numdam | MR | Zbl

[47] H.-M. Nguyen - Optimal constant in a new estimate for the degree, J. Anal. Math. 101 (2007), p. 367-395. | DOI | MR | Zbl

[48] L. Nirenberg - On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa 13 (1959), p. 115-162. | EuDML | Numdam | MR | Zbl

[49] C. W. Oseen - Beiträge zur Theorie anisotroper Flüssigkeiten, Arkiv för matematik, astronomi och fysik 19A (1925), p. 1-19. | Zbl

[50] J. G. Rešetnjak - Estimates of the modulus of continuity for certain mappings, Sibirsk. Mat. Ž. 7 (1966), p. 1106-1114. | MR | Zbl

[51] J. G. Rešetnjak, Mappings with bounded distortion as extremals of integrals of Dirichlet type, Sibirsk. Mat. Ž. 9 (1968), p. 652-666. | MR

[52] Y. G. Reshetnyak - Space mappings with bounded distortion, Translations of Mathematical Monographs, vol. 73, Amer. Math. Soc., 1989. | MR | Zbl

[53] D. Sarason - Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), p. 391-405. | DOI | MR | Zbl

[54] R. Schoen & K. Uhlenbeck - A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), p. 307-335. | DOI | MR | Zbl

[55] R. Schoen & K. Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983), p. 253-268. | DOI | MR | Zbl

[56] W. Sickel & A. Youssfi - The characterisation of the regularity of the Jacobian determinant in the framework of potential spaces, J. London Math. Soc. 59 (1999), p. 287-310. | DOI | MR | Zbl

[57] W. Sickel & A. Youssfi, The characterization of the regularity of the Jacobian determinant in the framework of Bessel potential spaces on domains, J. London Math. Soc. 60 (1999), p. 561-580. | DOI | MR | Zbl

[58] E. M. Stein - Note on the class L log L , Studio, Math. 32 (1969), p. 305-310. | EuDML | MR | Zbl

[59] E. M. Stein & G. Weiss - On the theory of harmonic functions of several variables. I. The theory of H p -spaces, Acta Math. 103 (1960), p. 25-62. | DOI | MR | Zbl

[60] L. Tartar - Compensated compactness and applications to partial differential equations, in Nonlinear analysis and mechanics : Heriot-Watt Symposium, Vol. IV, Res. Notes in Math., vol. 39, Pitman, 1979, p. 136-212. | MR | Zbl

[61] L. Tartar, The compensated compactness method applied to systems of conservation laws, in Systems of nonlinear partial differential equations (Oxford, 1982), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 111, Reidel, 1983, p. 263-285. | DOI | MR | Zbl

[62] L. Tartar, Remarks on oscillations and Stokes' equation, in Macroscopic modelling of turbulent flows (Nice, 1984), Lecture Notes in Phys., vol. 230, Springer, 1985, p. 24-31. | DOI | MR | Zbl

[63] A. Youssfi - Bilinear operators and the Jacobian-determinant on Besov spaces, Indiana Univ. Math. J. 45 (1996), p. 381-396. | DOI | MR | Zbl