Minimizing a functional depending on u and on u

Arrigo Cellina

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 3, page 339-352
  • ISSN: 0294-1449

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Cellina, Arrigo. "Minimizing a functional depending on $\nabla u$ and on $u$." Annales de l'I.H.P. Analyse non linéaire 14.3 (1997): 339-352. <http://eudml.org/doc/78414>.

@article{Cellina1997,
author = {Cellina, Arrigo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {existence of solutions; minimum problems},
language = {eng},
number = {3},
pages = {339-352},
publisher = {Gauthier-Villars},
title = {Minimizing a functional depending on $\nabla u$ and on $u$},
url = {http://eudml.org/doc/78414},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Cellina, Arrigo
TI - Minimizing a functional depending on $\nabla u$ and on $u$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 3
SP - 339
EP - 352
LA - eng
KW - existence of solutions; minimum problems
UR - http://eudml.org/doc/78414
ER -

References

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  2. [2] A. Cellina and S. Perrotta, On minima of radially symmetric functionals of the gradient, Nonlinear Analysis, TMA, Vol. 23, 1994, pp. 239-249. Zbl0819.49013MR1289130
  3. [3] A. Cellina and S. Perrotta, On a problem of Potential Wells, Journal of Convex Anal.z, Vol. 2, 1995, pp. 103-116. Zbl0880.49005MR1363363
  4. [4] A. Cellina and S. Zagatti, A version of Olech's Lemma in a Problem of the Calculus of Variations, SIAM J. Control and Optimization, Vol. 32, 1994, pp. 1114-1127. Zbl0874.49013MR1280232
  5. [5] A. Cellina and S. Zagatti, An Existence Result in a Problem of the Vectorial Case of the Calculus of Variations, SIAM J. Control and Optimization, Vol. 333, 1995. Zbl0822.49009MR1327245
  6. [6] B. Dacorogna and P. Marcellini, Existence of Minimizers for non quasiconvex integrals, Preprint Ecole Polytechnique Federale Lausanne, June 1994, to appear in: Arch. Rat. Mech. Anal. Zbl0837.49002MR1354700
  7. [7] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. Zbl0804.28001MR1158660
  8. [8] G. Friesecke, A necessary and sufficient condition for nonattainement and formation of microstructure almost everywhere in scalar variational problems, Proc. Royal Soc. Edinburgh, Vol. 124, 1984, pp. 437-471. Zbl0809.49017MR1286914
  9. [9] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. Zbl0361.35003MR473443
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  11. [11] B. Kawohl, J. Stara and G. Wittum, Analysis and Numerical Studies of a Problem of Shape Design, Arch. Rat. Mech. Anal., Vol. 114, 1991, pp. 349-363. Zbl0726.65071MR1100800
  12. [12] R.V. Kohn and G. Strang, Optimal Design and Relaxation of Variational Problems I, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 113-137. Zbl0609.49008MR820342
  13. [13] E. Mascolo and R. Schianchi, Existence Theorems for Nonconvex Problems, J. Math. Pures Appl., Vol. 62, 1983, pp. 349-359. Zbl0522.49001MR718948
  14. [14] F. Murat and L. Tartar, Calcul des variations et Homegenization, in: Les Méthodes de l'homogenization, Eds: D. Bergman et al., Collection de la Direction des Études et recherche de l'Électricité de France, Vol. 57, 1985, pp. 319-369. MR844873
  15. [15] R. Tahraoui, Sur une classe de fonctionnelles non convexes et applications, SIAM J. Math. Anal., Vol. 21, 1990, pp. 37-52. Zbl0738.73025MR1032726
  16. [16] R. Tahraoui, Théoremes d'existence en calcul des variations et applications a l'élasticité non lineaire, Proc. Royal Soc. Edinburgh, Vol. 109 A, 1988, pp. 51-78. Zbl0681.49004MR952329

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