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Novaga, Matteo:
Soluzioni di tipo barriera
Bollettino dell'Unione Matematica Italiana Serie 8 4-B (2001), fasc. n.1, p. 131-142, Unione Matematica Italiana (Italian)
pdf (448 Kb), djvu (157 Kb). | MR1821402 | Zbl 1072.35088

Sunto

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.
Referenze Bibliografiche
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[2] G. BELLETTINI-M. NOVAGA, Minimal barriers for geometric evolutions, J. Differential Eqs., 139 (1997), 76-103. | MR 1467354 | Zbl 0882.35028
[3] G. BELLETTINI-M. NOVAGA, Comparison results between minimal barriers and viscosity solutions for geometric evolutions, Ann. Sc. Norm. Sup. Pisa, XXVI (1998), 97-131. | fulltext mini-dml | MR 1632984 | Zbl 0904.35041
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[7] M. G. CRANDALL-H. ISHII-P. L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Am. Math. Soc., 27 (1992), 1-67. | fulltext mini-dml | MR 1118699 | Zbl 0755.35015
[8] M. G. CRANDALL-P. L. LIONS, Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, 277 (1983), 1-43. | MR 690039 | Zbl 0599.35024
[9] E. DE GIORGI, Barriers, boundaries, motion of manifolds, Conference held at Department of Mathematics of Pavia, March 18, 1994.
[10] P. L. LIONS, Generalized Solutions of Hamilton-Jacobi Equations, volume 69 of Research Notes in Math. Pitman, Boston, 1982. | MR 667669 | Zbl 0497.35001

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