On the lower semicontinuity of certain integral functionals

Ennio De Giorgi; Giuseppe Buttazzo; Gianni Dal Maso

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1983)

  • Volume: 74, Issue: 5, page 274-282
  • ISSN: 1120-6330

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De Giorgi, Ennio, Buttazzo, Giuseppe, and Dal Maso, Gianni. "On the lower semicontinuity of certain integral functionals." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 74.5 (1983): 274-282. <http://eudml.org/doc/287314>.

@article{DeGiorgi1983,
author = {De Giorgi, Ennio, Buttazzo, Giuseppe, Dal Maso, Gianni},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {integral functionals; lower semicontinuity; subdifferential},
language = {eng},
month = {5},
number = {5},
pages = {274-282},
publisher = {Accademia Nazionale dei Lincei},
title = {On the lower semicontinuity of certain integral functionals},
url = {http://eudml.org/doc/287314},
volume = {74},
year = {1983},
}

TY - JOUR
AU - De Giorgi, Ennio
AU - Buttazzo, Giuseppe
AU - Dal Maso, Gianni
TI - On the lower semicontinuity of certain integral functionals
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1983/5//
PB - Accademia Nazionale dei Lincei
VL - 74
IS - 5
SP - 274
EP - 282
LA - eng
KW - integral functionals; lower semicontinuity; subdifferential
UR - http://eudml.org/doc/287314
ER -

References

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  1. Castaing, C. and Valadier, M. (1977) - Convex analysis and measurable multifunctions. «Lecture Notes in Math.», 580, Springer-Verlag, Berlin. Zbl0346.46038MR467310
  2. Cesari, L. (1974) - Lower semicontinuity and lower closure theorems without seminormality conditions. «Ann. Mat. Pura Appl.», 98, 382-397. Zbl0281.49006MR344966
  3. De La Vallee Poussin, C.J. (1915) - Sur l'integrale de Lebesgue. «Trans. Amer. Math. Soc.», 16, 435-501. Zbl45.0441.06MR1501024DOI10.2307/1988879
  4. Ekeland, I. and Temam, R. (1978) - Convex analysis and variational problems. North-Holland, Amsterdam. Zbl0939.49002MR569206
  5. Ferro, F. (1981) - Lower semicontinuity, optimization and regularizing extensions of integral functionals. «SIAM J. Control Optim.», 19, 433-444. Zbl0473.49009MR618236DOI10.1137/0319025
  6. Marcus, M. and Mizel, V.J. (1972) - Absolute continuity on tracks and mappings of Sobolev spaces. «Arch. Rational. Mech. Anal.», 45, 294-320. Zbl0236.46033MR338765
  7. Morrey, C.B. (1966) - Multiple integrals in the Calculus of Variations. Springer-Verlag, Berlin. Zbl0142.38701MR202511
  8. Olech, C. (1976) - Weak lower semicontinuity of integral functionals. «J. Optimization Theory Appl.», 19, 3-16. Zbl0305.49019MR428161
  9. Serrin, J. (1961) - On the definition and properties of certain variational integrals. «Trans. Amer. Math. Soc.», 101, 139-167. Zbl0102.04601MR138018
  10. Serrin, J. and Varberg, D.E. (1969) - A general chain rule for derivatives and the change of variables formula for the Lebesgue integral. «Amer. Math. Monthly», 16, 514-520. Zbl0175.34401MR247011

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