- Attouch , H. 1984 . “ Variational convergence for functions and operators ” . London : Pitman .
- Ball , J. M. and Murat , F. 1984 . W1,p-quasiconvexity and variational problems for multiple integrals . J. Funct. Anal. , 58 : 221 – 253 .
- Bensoussan , A. , Lions , J. L. and Papanicolau , G. 1978 . “ Asymptotic analysis for periodic structures ” . North-Holland : Amsterdam .
- Boccardo , L. and Marcellini , P. 1976 . Sulla convergenza delle soluzioni di disequazioni variazionali . Ann. Mat. Pura Appl. , 110 ( 4 ) : 137 – 159 .
- Bouchite' , G. and Valadier , M. 1988 . Integral Representation of Convex Functionals on a Space of Measures . J. Funct. Anal. , 80 ( 4 ) : 398 – 420 .
- Buttazzo , G. 1989 . Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations . Longman, Scientific & Technical , 80 ( 4 )
- Carbone , L. and Sbordone , C. 1979 . Some properties of Γ-limits of integral functionals . Ann. Mat. Pura Appl. , 122 ( 4 ) : 1 – 60 .
- Cioranescu , D. and Murat , F. 1982 . “ Un terme étrange venu d'ailleurs, I & II; in Nonlinear Partial Differential Equations and Their Applications, Collège de France Séminar, Voll. II + III ” . In Reseach Notes in Mat. , Edited by: Brezis , H. and Lions , J. L. Vol. 60&70 , 98 – 138 . Pitman .
- 154 – 178 .
- A. Corbo Esposito R. De Arcangelis Comparison Results for Some Types of Relaxation of Variational Integral Functionals to appear on Ann. Mat. pura Appl.
- Corbo Esposito , A. , De ARcangelis , R. and Frattarolo , W. 1989 . “ Homogenization of variational integrals not coinciding with their relaxed functinals ” . In Preprint istituto di Fisica, Matematica ed informatica , Universitá di Salerno .
- Dacorogna , B. 1989 . “ Direct Methods in the Calculus of Variations ” . In Applied Mathematical Sciences , Berlin : Springer Verlag .
- Dal Maso , G. and Modica , L. 1986 . Nonlinear stochastic homogenization . Ann. Mat. Pura Appl. , 144 ( 4 ) : 347 – 389 .
- De Arcangelis , R. 1991 . A General Homogenization Result for Almost Periodic Functionals . J. Math. Anal. Appl. , 156 ( 2 ) : 358 – 380 .
- De Arcangelis , R. 1989 . Some remarks on the identity between a variational integral and its relaxed functionsl . Ann. Univ. Ferrara - Sez. VII - Sc. Mat. , 35 ( 2 ) : 135 – 145 .
- De Arcangelis , R. and Donato , P. 1985 . Homogenization in weighted Sobolev spaces . Ricerche Mat. , 36 ( 2 ) : 289 – 308 .
- De Giorgi , E. and Franzoni , C. 1979 . Su un tipo di convergenza variazionale . Rend. Sem. Mat. Brescia , 3 ( 2 ) : 63 – 101 .
- De Giorgi , E. and Spagnolo , S. 1973 . Sulla convergenza degli integrali dell'energia per operatori ellittici del secondo ordine . Boll. Unione Mat. Ital. , 8 ( 4 ) : 391 – 411 .
- Dunford , N. and Schwartz , S. 1957 . Linear Operators . Wiley-Interscience Publiations , 8 ( 4 )
- Ekeland , I. and Temam , R. 1976 . Convex Analysis and Variational Problems . North Holland American Elsevier , 8 ( 4 )
- Giaquinta , M. , Modica , G. and Souocek , J. 1979 . Functionals with linear growth in the Calculus of Variations I . Comment. Math. Univ. Carolinae , 20 ( 4 ) : 143 – 156 .
- Giusti , E. 1984 . “ Minimal Surfaces and Functions of Bounded Variations ” . Basel : Birkäuser-Verlag .
- Goffman , C. and Serrin , J. 1964 . Subllinear functions of measures and variational integrals . Duke Math. J. , 31 : 159 – 178 .
- Lavrentieff , M. 1926 . Sur quelques problèmes du calcul des variations . Ann. Mat. Pura Appl. , 4 : 7 – 29 .
- Mania , B. 1934 . Sopra un esempio di Lavrentieff . Boll. Unione Mat. Ital. , 13 : 147 – 153 .
- Marcellini , P. and Sbordone , C. 1978 . Homogenization of non uniformly elliptic operators . Appl. Anal. , 8 : 103 – 113 .
- Sbordone , C. 1975 . Su alcune applicazioni di un tipoo di convergenza variazionale . Ann. Scu. Norm. Sup. Pisa , 2 : 617 – 638 .
- Serrin , J. 1961 . On the definitiono and properties of certain variational integrals . Trans. Amer. Math. Soc. , 101 : 139 – 167 .
- A. Corbo Esposito R. De Arcangelis Comparison Results for Some Types of Relaxation of Variational Integral Functionals $title:to appear on Ann. Mat. pura Appl. L. Tartar Cours Peccot au Collège de France
- Zhikov , V. 1987 . Averaging of Functionals in Calculus of Variations and Elasticity Theory . Math. USSR Izvestiya , 29 : 33 – 66 .
The Lavrentieff phenomenon And Different processes of Homogenization
Reprints and Corporate Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
To request a reprint or corporate permissions for this article, please click on the relevant link below:
Academic Permissions
Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?
Obtain permissions instantly via Rightslink by clicking on the button below:
If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.
Related research
People also read lists articles that other readers of this article have read.
Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.
Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.