Pattern evolution

Augusto Visintin

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)

  • Volume: 17, Issue: 2, page 197-225
  • ISSN: 0391-173X

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Visintin, Augusto. "Pattern evolution." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.2 (1990): 197-225. <http://eudml.org/doc/84071>.

@article{Visintin1990,
author = {Visintin, Augusto},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {generalized coarea formula; boundary of fractional dimension; morphogenesis; hysteresis; two-phase systems; surface tension; pattern interpolation},
language = {eng},
number = {2},
pages = {197-225},
publisher = {Scuola normale superiore},
title = {Pattern evolution},
url = {http://eudml.org/doc/84071},
volume = {17},
year = {1990},
}

TY - JOUR
AU - Visintin, Augusto
TI - Pattern evolution
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 2
SP - 197
EP - 225
LA - eng
KW - generalized coarea formula; boundary of fractional dimension; morphogenesis; hysteresis; two-phase systems; surface tension; pattern interpolation
UR - http://eudml.org/doc/84071
ER -

References

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  2. [2] E. De Giorgi, Su una teoria generale della misura (r-1) dimensionale in uno spazio r dimensioni, Ann. Mat. Pura Appl. (4), 36 (1954), 191-213. Zbl0055.28504MR62214
  3. [3] E. De Giorgi - F. Colombini - L.C. Piccinini, Frontiere orientate di misura minima e questioni collegate, Scuola Norm. Sup., Pisa (1972). Zbl0296.49031MR493669
  4. [4] G. Dziuk, Finite element method for the Beltrami operator on arbitrary surfaces, in Partial differential equations and calculus of variations (S. Hildebrandt, R. Leis, eds.), Lecture Notes in Math., Springer, Berlin (1988). Zbl0663.65114
  5. [5] H. Federer, Geometric measure theory, Springer-Verlag, Berlin (1969). Zbl0176.00801MR257325
  6. [6] W.H. Fleming - R. Rishel, An integral formula for total gradient variation, Arch. Math., 11 (1960), 218-222. Zbl0094.26301MR114892
  7. [7] E. Giusti, Minimal surfaces and functions of bounded variation, Birkhäuser, Boston (1984). Zbl0545.49018MR775682
  8. [8] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom., 20 (1984), 237-266. Zbl0556.53001MR772132
  9. [9] G. Huisken, Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature, Invent. Math., 84 (1986), 463-480. Zbl0589.53058MR837523
  10. [10] G. Huisken, Deforming hypersurfaces of the sphere by their mean curvature, Math. Z., 195 (1987), 205-219. Zbl0626.53039MR892052
  11. [11] A Krasnosel'skiĭ - A.V. Pokrovski, Systems with hysteresis (Russian), Nauka, Moskow (1983). English Translation: Springer, Berlin (1989). MR742931
  12. [12] A. Visintin, Mathematical models of hysteresis, in Topics in Non-smooth Mechanics (J.J. Moreau, G. Strang. P.D. Panagiotopoulos, Ed.s), Birkhäuser, Basel (1988). Zbl0656.73043MR957094
  13. [13] A. Visintin, Surface tension effects in phase transitions, in "Material Instabilities in Continuum Mechanics and Related Mathematical Problems" (J. Ball., ed.), Clarendon Press, Oxford (1988), 505-537. Zbl0648.73050MR970541
  14. [14] A. Visintin, Non-convex functionals related to multi-phase system, S.I.A.M. J. Math. Anal., September 1990 (in press). 
  15. [15] A. Visintin, Surface tension effects in two-phase systems, in Proceedings of the Colloquium on Free Boundary Problems held in Irsee in June 1987 (to appear). MR1081763
  16. [16] A. Visintin, Generalized coarea formula and fractal sets. Japan J. Appl. Math. (to appear). Zbl0736.49030MR1111612
  17. [17] A. Visintin, Generalized coarea formula, In "Recent Advances in Nonlinear Elliptic and Parabolic Problems" (P. Benilan, M. Chipot, L.C. Evans and M. Pierre, eds.), Longman, Harlow (1989). MR1035019
  18. [18] A. Visintin, Models of pattern formation, C.R. Acad. Sci. Paris, 309 (1989), Série I, 429-434. Zbl0749.49026MR1054267

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