An explicit solution to a system of implicit differential equations

Bernard Dacorogna; Paolo Marcellini; Emanuele Paolini

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 1, page 163-171
  • ISSN: 0294-1449

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Dacorogna, Bernard, Marcellini, Paolo, and Paolini, Emanuele. "An explicit solution to a system of implicit differential equations." Annales de l'I.H.P. Analyse non linéaire 25.1 (2008): 163-171. <http://eudml.org/doc/78778>.

@article{Dacorogna2008,
author = {Dacorogna, Bernard, Marcellini, Paolo, Paolini, Emanuele},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {almost everywhere solutions; vectorial pyramids},
language = {eng},
number = {1},
pages = {163-171},
publisher = {Elsevier},
title = {An explicit solution to a system of implicit differential equations},
url = {http://eudml.org/doc/78778},
volume = {25},
year = {2008},
}

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
PB - Elsevier
VL - 25
IS - 1
SP - 163
EP - 171
LA - eng
KW - almost everywhere solutions; vectorial pyramids
UR - http://eudml.org/doc/78778
ER -

References

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  3. [3] Cellina A., On the differential inclusion x ' ∈ { - 1 , 1 } , Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.69 (1980) 1-6. Zbl0922.34009MR641583
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  6. [6] Cellina A., Perrotta S., On a problem of potential wells, J. Convex Anal.2 (1995) 103-115. Zbl0880.49005MR1363363
  7. [7] Dacorogna B., Marcellini P., General existence theorems for Hamilton–Jacobi equations in the scalar and vectorial case, Acta Math.178 (1997) 1-37. Zbl0901.49027MR1448710
  8. [8] Dacorogna B., Marcellini P., Implicit Partial Differential Equations, Progress in Nonlinear Differential Equations and Their Applications, vol. 37, Birkhäuser, 1999. Zbl0938.35002MR1702252
  9. [9] Dacorogna B., Pisante G., A general existence theorem for differential inclusions in the vector valued case, Portugal. Math.62 (2005) 421-436. Zbl1107.49008MR2191629
  10. [10] De Blasi F.S., Pianigiani G., Non convex valued differential inclusions in Banach spaces, J. Math. Anal. Appl.157 (1991) 469-494. Zbl0728.34013MR1112329
  11. [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. A124 (1994) 437-471. Zbl0809.49017MR1286914
  12. [12] R.D. James, unpublished work. 
  13. [13] B. Kirchheim, Rigidity and geometry of microstructures, Preprint Max-Plank-Institut, Leipzig, Lecture Note 16, 2003. Zbl1140.74303
  14. [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. Zbl0930.35038MR1449410

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