Soluzioni di tipo barriera
Novaga, Matteo
Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 131-142 / Harvested from Biblioteca Digitale Italiana di Matematica
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We present the general theory of barrier solutions in the sense of De Giorgi, and we consider different applications to ordinary and partial differential equations. We discuss, in particular, the case of second order geometric evolutions, where the barrier solutions turn out to be equivalent to the well-known viscosity solutions.

Publié le : 2001-02-01
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     author = {Matteo Novaga},
     title = {Soluzioni di tipo barriera},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {131-142},
     zbl = {1072.35088},
     mrnumber = {1821402},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_1_131_0}
}

Novaga, Matteo. Soluzioni di tipo barriera. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 131-142. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_1_131_0/

[1] Ambrosio, L., Lecture Notes on Geometric Evolution Problems, Distance Function and Viscosity Solutions, in Proc. of the School on Calculus of Variation, Pisa 1996, Springer-Verlag, Berlin, 1999. | MR 1757696 | Zbl 0956.35002

[2] Bellettini, G.-Novaga, M., Minimal barriers for geometric evolutions, J. Differential Eqs., 139 (1997), 76-103. | MR 1467354 | Zbl 0882.35028

[3] Bellettini, G.-Novaga, M., Comparison results between minimal barriers and viscosity solutions for geometric evolutions, Ann. Sc. Norm. Sup. Pisa, XXVI (1998), 97-131. | MR 1632984 | Zbl 0904.35041

[4] Bellettini, G.-Novaga, M., Some aspects of De Giorgi's barriers for geometric evolutions, in Proc. of the School on Calculus of Variation, Pisa 1996, Springer-Verlag, Berlin, 1999. | MR 1757698 | Zbl 0957.35080

[5] Bellettini, G.-Paolini, M., Some results on minimal barriers in the sense of De Giorgi applied to driven motion by mean curvature, Rend. Accad. Naz. Sci. XL Mem. Mat., 19 (1995), 43-67. | MR 1387549 | Zbl 0944.53039

[6] Chen, Y.-G.-Giga, Y.-Goto, S., Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom., 33 (1991), 749-786. | MR 1100211 | Zbl 0696.35087

[7] Crandall, M. G.-Ishii, H.-Lions, P. L., User's guide to viscosity solutions of second order partial differential equations, Bull. Am. Math. Soc., 27 (1992), 1-67. | MR 1118699 | Zbl 0755.35015

[8] Crandall, M. G.-Lions, P. L., Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, 277 (1983), 1-43. | MR 690039 | Zbl 0599.35024

[9] De Giorgi, E., Barriers, boundaries, motion of manifolds, Conference held at Department of Mathematics of Pavia, March 18, 1994.

[10] Lions, P. L., Generalized Solutions of Hamilton-Jacobi Equations, volume 69 of Research Notes in Math. Pitman, Boston, 1982. | MR 667669 | Zbl 0497.35001