# A variational inequality for discontinuous solutions of degenerate parabolic equations.

Lorina Dascal; Shoshana Kamin; Nir A. Sochen

RACSAM (2005)

- Volume: 99, Issue: 2, page 243-256
- ISSN: 1578-7303

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topDascal, 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 -