Minkowski-Bouligand dimension of solutions of the one-dimensional p-Laplacian

Journal of Differential Equations

Volumn 190, Issue 1, 2003, Pages 268-305

  Pašić, Mervan ^a  

^a UNIVERSITY OF ZAGREB   (Croatia)

Author keywords

Change of dimension; Fractal dimension; Graph; Nonlinear p Laplacian; Order of growth of singularity; Qualitative properties; Quasilinear equations

Indexed keywords

EID: 0037691742     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(02)00149-3     Document Type: Article

References (21)

1. G. Bouligand, Dimension, Etendue, Densité, C. R. Acad. Sci. Paris 180 (1925) 246-248.
2. H. Brezis, Analyse fonctionelle. Théorie et applications, Masson, Paris, 1983.
3. C. Dubuc, C. Tricot, Variation d'une fonction et dimension de son graphe, C. R. Acad. Sci. Paris 306 (1988) 531-533.
4. K. Falconer, Fractal Geometry. Mathematical Foundations and Applications, Willey, New York, 1999.
5. L. Korkut, M. Pašić, D. Žubrinić, Control of essential infimum and supremum of solutions of quasilinear elliptic equations, C. R. Acad. Sci. Paris 329 (1999) 269-274.
6. L. Korkut, M. Pašić, D. Žubrinić, Some qualitative properties of solutions of quasilinear elliptic equations and applications, J. Differential Equations 170 (2001) 247-280.
7. A. Le Méhauté, Fractal Geometries. Theory and Applications, Hermes, Paris, 1990.
8. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
9. A. Lomtatidze, L. Malaguti, On a two-point boundary value problem for the second order ordinary differential equations with singularities, Nonlinear Anal. TMA 52 (2003) 1553-1567.
10. P. Matila, Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability, Cambridge Univ. Press, Cambridge, 1995.
11. D. O'Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer, Dordrecht, 1997.
12. M. Pašić, Isoperimetric inequalities in quasilinear elliptic equations of Leray-Lions type, J. Math. Pures Appl. 75 (1996) 343-366.
13. M. Pašić, Fractional dimension of solutions for several types of nonlinear b.v.p.'s associated to the one dimensional p-Laplacian, in preparation.
14. H.O. Peitgen, H. Jurgens, D. Saupe, Chaos and Fractals. New Frontiers of Science, Springer, Berlin, 1992.
15. p dy and T in the equation P(u) = T, J. Differential Equations 86 (1990) 102-122.
16. J.M. Rakotoson, R. Temam, A co-area formula with applications to monotone rearrangement and to regularity, Arch. Rational Mech. Anal. 109 (1990) 213-238.
17. G. Talenti, Linear elliptic P.D.E.'s: level sets, rearrangements and a priori estimates of solutions, Boll. UMI 64-B (1985) 917-949.
18. C. Tricot, Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc. 91 (1982) 57-74.
19. C. Tricot, Dimension de graphes, C. R. Acad. Sci. Paris 303 (1986) 609-612.
20. C. Tricot, Curves and Fractal Dimension, Springer, Berlin, 1995.
21. C. Tricot, Formule integrale pour la dimension fractale dans le plan, C. R. Acad. Sci. Paris 333 (2001) 169-172.