An explicit solution to a system of implicit differential equations
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 163-171. 
@article{AIHPC_2008__25_1_163_0,
     author = {Dacorogna, Bernard and Marcellini, Paolo and Paolini, Emanuele},
     title = {An explicit solution to a system of implicit differential equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {163--171},
     publisher = {Elsevier},
     volume = {25},
     number = {1},
     year = {2008},
     doi = {10.1016/j.anihpc.2006.11.007},
     mrnumber = {2383084},
     zbl = {1141.35014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.007/}
}
TY  - JOUR
AU  - Dacorogna, Bernard
AU  - Marcellini, Paolo
AU  - Paolini, Emanuele
TI  - An explicit solution to a system of implicit differential equations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2008
SP  - 163
EP  - 171
VL  - 25
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.007/
DO  - 10.1016/j.anihpc.2006.11.007
LA  - en
ID  - AIHPC_2008__25_1_163_0
ER  - 
%0 Journal Article
%A Dacorogna, Bernard
%A Marcellini, Paolo
%A Paolini, Emanuele
%T An explicit solution to a system of implicit differential equations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2008
%P 163-171
%V 25
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.007/
%R 10.1016/j.anihpc.2006.11.007
%G en
%F AIHPC_2008__25_1_163_0
Dacorogna, Bernard; Marcellini, Paolo; Paolini, Emanuele. An explicit solution to a system of implicit differential equations. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 163-171. doi : 10.1016/j.anihpc.2006.11.007. http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.007/

[1] Ball J.M., James R.D., Fine phase mixtures as minimizers of energy, Arch. Ration. Mech. Anal. 100 (1987) 15-52. | MR | Zbl

[2] Bressan A., Flores F., On total differential inclusions, Rend. Sem. Mat. Univ. Padova 92 (1994) 9-16. | Numdam | MR | Zbl

[3] Cellina A., On the differential inclusion x ' ∈{-1,1}, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 69 (1980) 1-6. | MR | Zbl

[4] Cellina A., On minima of a functional of the gradient: necessary conditions, Nonlinear Anal. 20 (1993) 337-341. | MR | Zbl

[5] Cellina A., On minima of a functional of the gradient, sufficient conditions, Nonlinear Anal. 20 (1993) 343-347. | MR | Zbl

[6] Cellina A., Perrotta S., On a problem of potential wells, J. Convex Anal. 2 (1995) 103-115. | MR | Zbl

[7] Dacorogna B., Marcellini P., General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial case, Acta Math. 178 (1997) 1-37. | MR | Zbl

[8] Dacorogna B., Marcellini P., Implicit Partial Differential Equations, Progress in Nonlinear Differential Equations and Their Applications, vol. 37, Birkhäuser, 1999. | MR | Zbl

[9] Dacorogna B., Pisante G., A general existence theorem for differential inclusions in the vector valued case, Portugal. Math. 62 (2005) 421-436. | MR | Zbl

[10] De Blasi F.S., Pianigiani G., Non convex valued differential inclusions in Banach spaces, J. Math. Anal. Appl. 157 (1991) 469-494. | MR | Zbl

[11] Friesecke G., A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994) 437-471. | MR | Zbl

[12] R.D. James, unpublished work.

[13] B. Kirchheim, Rigidity and geometry of microstructures, Preprint Max-Plank-Institut, Leipzig, Lecture Note 16, 2003.

[14] Müller S., Sverak V., Attainment results for the two-well problem by convex integration, in: Jost J. (Ed.), Geometric Analysis and the Calculus of Variations, International Press, 1996, pp. 239-251. | MR | Zbl

Cité par Sources :