Lower semicontinuity of L∞ functionals

E. N. Barron; R. R. Jensen; C. Y. Wang

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 4, page 495-517
  • ISSN: 0294-1449

How to cite

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Barron, E. N., Jensen, R. R., and Wang, C. Y.. "Lower semicontinuity of L∞ functionals." Annales de l'I.H.P. Analyse non linéaire 18.4 (2001): 495-517. <http://eudml.org/doc/78529>.

@article{Barron2001,
author = {Barron, E. N., Jensen, R. R., Wang, C. Y.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {lower semicontinuity; Morrey convexity; Morrey quasiconvexity; polyquasiconvexity; rank-one quasiconvexity; levelconvexity},
language = {eng},
number = {4},
pages = {495-517},
publisher = {Elsevier},
title = {Lower semicontinuity of L∞ functionals},
url = {http://eudml.org/doc/78529},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Barron, E. N.
AU - Jensen, R. R.
AU - Wang, C. Y.
TI - Lower semicontinuity of L∞ functionals
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 4
SP - 495
EP - 517
LA - eng
KW - lower semicontinuity; Morrey convexity; Morrey quasiconvexity; polyquasiconvexity; rank-one quasiconvexity; levelconvexity
UR - http://eudml.org/doc/78529
ER -

References

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  1. [1] Aronsson G., Minimization problems for the functional supxF(x,f(x),f′(x)), Ark. Mat.6 (1965) 33-53. Zbl0156.12502
  2. [2] Aronsson G., Extension of functions satisfying Lipschitz conditions, Ark. Mat.6 (28) (1967) 551-561. Zbl0158.05001MR217665
  3. [3] Aronsson G., Minimization problems for the functional supxF(x,f(x),f′(x)). III, Ark. Mat.7 (1969) 509-512. Zbl0181.11902
  4. [4] Ball J., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal.63 (1977) 337-403. Zbl0368.73040MR475169
  5. [5] Barron E.N., Viscosity solutions and analysis in L∞, in: Nonlinear Analysis, Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic, Dordrecht, 1999, pp. 1-60. Zbl0973.49024
  6. [6] Barron E.N., Ishii H., The Bellman equation for minimizing the maximum cost, Nonlinear Anal.13 (9) (1989) 1067-1090. Zbl0691.49030MR1013311
  7. [7] Barron E.N., Jensen R., Liu W., Hopf–Lax-type formula for ut+H(u,Du)=0, J. Differential Equations126 (1) (1996) 48-61. Zbl0857.35023
  8. [8] Barron E.N., Liu W., Calculus of variations in L∞, Appl. Math. Optim.35 (3) (1997) 237-263. Zbl0871.49017
  9. [9] Dacorogna B., Direct Methods in the Calculus of Variations, Springer Verlag, New York, 1989. Zbl0703.49001MR990890
  10. [10] Ioffe A.D., On lower semicontinuity of integral functionals, SIAM J. Control Optim.15 (1977) 521-538. Zbl0361.46037MR637234
  11. [11] Ioffe A.D., Tikhomirov V.M., Theory of Extremal Problems, North-Holland, Amsterdam, 1979. Zbl0407.90051MR528295
  12. [12] Jensen R., Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient, Arch. Rat. Mech. Anal.123 (1993) 51-74. Zbl0789.35008MR1218686
  13. [13] Pedregal P., Paramaterized Measures and Variational Principles, Birkhauser, Boston, 1997. Zbl0879.49017MR1452107
  14. [14] Sverak V., Rank-one quasiconvexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh120A (1992) 185-189. Zbl0777.49015MR1149994

Citations in EuDML Documents

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  1. Changyou Wang, Yifeng Yu, C 1 -regularity of the Aronsson equation in R 2
  2. Michele Gori, Francesco Maggi, On the lower semicontinuity of supremal functionals
  3. Thierry Champion, Luigi De Pascale, Francesca Prinari, Γ -convergence and absolute minimizers for supremal functionals
  4. Michele Gori, On the lower semicontinuity of supremal functionals defined on measures
  5. Michele Gori, Francesco Maggi, On the Lower Semicontinuity of Supremal Functionals
  6. Thierry Champion, Luigi De Pascale, Francesca Prinari, -convergence and absolute minimizers for supremal functionals

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