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. Thierry Champion, Luigi De Pascale, Francesca Prinari, -convergence and absolute minimizers for supremal functionals
  6. Michele Gori, Francesco Maggi, On the Lower Semicontinuity of Supremal Functionals

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