Barriers for a class of geometric evolution problems
Giovanni Bellettini; Matteo Novaga
- Volume: 8, Issue: 2, page 119-128
- ISSN: 1120-6330
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topBellettini, Giovanni, and Novaga, Matteo. "Barriers for a class of geometric evolution problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.2 (1997): 119-128. <http://eudml.org/doc/244151>.
@article{Bellettini1997,
abstract = {We present some general results on minimal barriers in the sense of De Giorgi for geometric evolution problems. We also compare minimal barriers with viscosity solutions for fully nonlinear geometric problems of the form \( u\_\{t\} + F(t, x, \nabla u, \nabla^\{2\} u) = 0 \). If \( F \) is not degenerate elliptic, it turns out that we obtain the same minimal barriers if we replace \( F \) with \( F^\{+\} \), which is defined as the smallest degenerate elliptic function above \( F \).},
author = {Bellettini, Giovanni, Novaga, Matteo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Barriers; Nonlinear partial differential equations of parabolic type; Mean curvature flow; Viscosity solutions; minimal barriers; geometric evolution equations; viscosity solutions},
language = {eng},
month = {7},
number = {2},
pages = {119-128},
publisher = {Accademia Nazionale dei Lincei},
title = {Barriers for a class of geometric evolution problems},
url = {http://eudml.org/doc/244151},
volume = {8},
year = {1997},
}
TY - JOUR
AU - Bellettini, Giovanni
AU - Novaga, Matteo
TI - Barriers for a class of geometric evolution problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/7//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 2
SP - 119
EP - 128
AB - We present some general results on minimal barriers in the sense of De Giorgi for geometric evolution problems. We also compare minimal barriers with viscosity solutions for fully nonlinear geometric problems of the form \( u_{t} + F(t, x, \nabla u, \nabla^{2} u) = 0 \). If \( F \) is not degenerate elliptic, it turns out that we obtain the same minimal barriers if we replace \( F \) with \( F^{+} \), which is defined as the smallest degenerate elliptic function above \( F \).
LA - eng
KW - Barriers; Nonlinear partial differential equations of parabolic type; Mean curvature flow; Viscosity solutions; minimal barriers; geometric evolution equations; viscosity solutions
UR - http://eudml.org/doc/244151
ER -
References
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