Lower semicontinuity of a class of multiple integrals below the growth exponent

Flavia Giannetti; Anna Verde

Annales de la Faculté des sciences de Toulouse : Mathématiques (2001)

  • Volume: 10, Issue: 2, page 299-311
  • ISSN: 0240-2963

How to cite

top

Giannetti, Flavia, and Verde, Anna. "Lower semicontinuity of a class of multiple integrals below the growth exponent." Annales de la Faculté des sciences de Toulouse : Mathématiques 10.2 (2001): 299-311. <http://eudml.org/doc/73548>.

@article{Giannetti2001,
author = {Giannetti, Flavia, Verde, Anna},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {lower semicontinuity; mulptiple integrals; integral functional},
language = {eng},
number = {2},
pages = {299-311},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Lower semicontinuity of a class of multiple integrals below the growth exponent},
url = {http://eudml.org/doc/73548},
volume = {10},
year = {2001},
}

TY - JOUR
AU - Giannetti, Flavia
AU - Verde, Anna
TI - Lower semicontinuity of a class of multiple integrals below the growth exponent
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2001
PB - UNIVERSITE PAUL SABATIER
VL - 10
IS - 2
SP - 299
EP - 311
LA - eng
KW - lower semicontinuity; mulptiple integrals; integral functional
UR - http://eudml.org/doc/73548
ER -

References

top
  1. [1] Acerbi ( E.), Dal Maso ( G.). - New lower semicontinuity results for polyconvex integrals, Calc. Var. Partial Differential Equations2 (1994), no.3, 329-371. Zbl0810.49014MR1385074
  2. [2] Acerbi ( E.), Fusco ( N.). - Semicontinuity problems in the Calculus of Variations, Arch. Rat. Mech. Anal.86 (1984), 125-145. Zbl0565.49010MR751305
  3. [3] Ball ( J.M.). - Convexity conditions and existence theorems in nonlinear elsticity, Arch. Rational Mech. Anal.63 (1977), 337-403. Zbl0368.73040MR475169
  4. [4] Ball ( J.M.), Murat ( F.). - W1,p quasiconvexity and variational problems for multiple integrals, J. Funct. Anal.58 (1984), 225-253. Zbl0549.46019MR759098
  5. [5] Dacorogna ( B.). — Direct Methods in the Calculus of Variations, Springer Verlag, Berlin (1989). Zbl0703.49001MR990890
  6. [6] Dacorogna ( B.), Marcellini ( P.). - Semicontinuité pour des intégrandes polyconvexes sans continuité des déterminants, C.R. Acad. Sci.Paris, 311 (1990), 393-396. Zbl0723.49007MR1071650
  7. [7] Dal Maso ( G.), Sbordone ( C.). - Weak lower semicontinuity of polyconvex integrals : a borderline case, Math. Z.218 (1995), no.4, 603-609. Zbl0822.49010MR1326990
  8. [8] Ekeland ( I.), Temam ( R.). - Convex Analysis and Variational Problems, North-Holland, New York (1976). Zbl0322.90046MR463994
  9. [9] Evans ( L.C.), Gariepy ( R.F.). — Measure theory and fine properties of functions,Studies in Advanced Maths.CRC Press1992. Zbl0804.28001MR1158660
  10. [10] Fonseca ( I.), Müller ( S.). - A-quasiconvexity, lower semicontinuity and Young measures, SIAM J. Math. Anal.30 (1999), n.6, 1355-1390. Zbl0940.49014MR1718306
  11. [11] Fonseca ( I.), Malý ( J.). - Relaxation of multiple integrals below the growth exponents, Ann. Inst. H. Poincaré14, n.3 (1997), 309-338. Zbl0868.49011MR1450951
  12. [12] Fonseca ( I.), Marcellini ( P.). - Relaxation of multiple integrals in subcritical Sobolev spaces, J. Geom. Anal.7 (1997), no.1, 57-81. Zbl0915.49011MR1630777
  13. [13] Fusco ( N.), Hutchinson ( J.E.). — A direct proof for lower semicontinuity of polyconvex functionals, Manu- scripta Math.87 (1995), 35-50. Zbl0874.49015MR1329439
  14. [14] Gangbo ( W.). - On the weak lower semicontinuity of energies with polyconvex integrandsJ. Math. Pures et Appl.73 (1994), 455-469. Zbl0829.49011MR1300984
  15. [15] Giannetti ( F.), Verde ( A.). - Variational Integrals for Elliptic Complexes, Studia Math.140 (2000), no.1, 79-98. Zbl0968.58019MR1763883
  16. [16] Iwaniec ( T.), Sbordone ( C.). - Quasiharmonic Fields, Ann. Inst. H. Poincaré Anal. Non Linéaire18, n. 5 (2001), 519-572. Zbl1068.30011MR1849688
  17. [17] Kristensen ( J.). - Finite Functionals and Young Measures Generated by Gradients of Sobolev Functions , Mat- Report 1994-34, Mathematical Institute, Technical University of Denmark, Lyngby, Denmark,1994. 
  18. [18] Malý ( J.). — Weak lower semicontinuity of polyconvex integrands, Proc. Royal Soc. Edin.123A (1993), 681-691. Zbl0813.49017MR1237608
  19. [19] Marcellini ( P.). - On the definition and lower semicontinuity of certain quasiconvex integrals, Ann. Inst. H. Poincaré (1986), 391-409. Zbl0609.49009MR868523
  20. [20] Meyers ( N.G.). - Quasiconvexity and the semicontinuity of multiple integrals of any order, Trans. Amer. Math. Soc.119 (1965), 125-149. Zbl0166.38501MR188838
  21. [21] Morrey ( C.B..). — Quasiconvexity and the semicontinuity of multiple integralsPacific J. Math.2 (1952), 25-53. Zbl0046.10803MR54865
  22. [22] Morrey ( C.B.). — Multiple integrals in the calculus of variationsDie Grund. der Math. Wiss.130, Springer Verlag, Heidelberg and New York, 1966. Zbl0142.38701MR202511

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.