Soluzioni di tipo barriera

Matteo Novaga

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 1, page 131-142
  • ISSN: 0392-4041

Abstract

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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.

How to cite

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Novaga, Matteo. "Soluzioni di tipo barriera." Bollettino dell'Unione Matematica Italiana 4-B.1 (2001): 131-142. <http://eudml.org/doc/195110>.

@article{Novaga2001,
author = {Novaga, Matteo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {2},
number = {1},
pages = {131-142},
publisher = {Unione Matematica Italiana},
title = {Soluzioni di tipo barriera},
url = {http://eudml.org/doc/195110},
volume = {4-B},
year = {2001},
}

TY - JOUR
AU - Novaga, Matteo
TI - Soluzioni di tipo barriera
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/2//
PB - Unione Matematica Italiana
VL - 4-B
IS - 1
SP - 131
EP - 142
LA - ita
UR - http://eudml.org/doc/195110
ER -

References

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  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. Zbl0956.35002MR1757696
  2. BELLETTINI, G.- NOVAGA, M., Minimal barriers for geometric evolutions, J. Differential Eqs., 139 (1997), 76-103. Zbl0882.35028MR1467354
  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. Zbl0904.35041MR1632984
  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. Zbl0957.35080MR1757698
  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. Zbl0944.53039MR1387549
  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. Zbl0696.35087MR1100211
  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. Zbl0755.35015MR1118699
  8. CRANDALL, M. G.- LIONS, P. L., Viscosity solutions of Hamilton-Jacobi equations, Trans. AMS, 277 (1983), 1-43. Zbl0599.35024MR690039
  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. Zbl0497.35001MR667669

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