A variational inequality for discontinuous solutions of degenerate parabolic equations.

Dascal, Lorina, Kamin, Shoshana, and Sochen, Nir A.. "A variational inequality for discontinuous solutions of degenerate parabolic equations.." RACSAM 99.2 (2005): 243-256. <http://eudml.org/doc/41016>.

@article{Dascal2005,
abstract = {The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem associated with the minimal surface equation.},
author = {Dascal, Lorina, Kamin, Shoshana, Sochen, Nir A.},
journal = {RACSAM},
keywords = {Ecuaciones parabólicas; Ecuaciones en derivadas parciales no lineales; Inecuaciones variacionales; Solución débil; Teorema de existencia; Unicidad; Funciones de variación acotada; generalization of Temam's definition of weak solution; variational inequality; Beltrami flow; BV space},
language = {eng},
number = {2},
pages = {243-256},
title = {A variational inequality for discontinuous solutions of degenerate parabolic equations.},
url = {http://eudml.org/doc/41016},
volume = {99},
year = {2005},
}

TY - JOUR
AU - Dascal, Lorina
AU - Kamin, Shoshana
AU - Sochen, Nir A.
TI - A variational inequality for discontinuous solutions of degenerate parabolic equations.
JO - RACSAM
PY - 2005
VL - 99
IS - 2
SP - 243
EP - 256
AB - The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem associated with the minimal surface equation.
LA - eng
KW - Ecuaciones parabólicas; Ecuaciones en derivadas parciales no lineales; Inecuaciones variacionales; Solución débil; Teorema de existencia; Unicidad; Funciones de variación acotada; generalization of Temam's definition of weak solution; variational inequality; Beltrami flow; BV space
UR - http://eudml.org/doc/41016
ER -