Parabolic Quasilinear Equations Minimizing Linear Growth Functionals
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Beschreibung
This book covers with great detail the mathematical developments in total variation based image restauration. It contains a full analysis of quasilinear parabolic equations whose operator is in divergence form, being the subdifferential of a convex function of the modulus of the gradient.
The techniques can be used to justify many mathematical models appearing in different contexts like continuum mechanics, faceted crystal growth, and image processing. The book will be useful to graduate students and researchers in mathematics and image processing.
Covers with great detail the mathematical developments in total variation based image restauration Contains a full analysis of quasilinear parabolic equations whose operator is in divergence form, being the subdifferential of a convex function of the modulus of the gradient
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Fuensanta Andreu-Vaillo
Themen in »Parabolic Quasilinear Equations Minimizing Linear Growth Functionals«
Approximation Calculus of variations Dirichlet problem Image restoration Neumann problem Nonlinear semigroups Parabolic equations partial differential equation partial differential equations
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"This book is well written…[and] should be of interest to anyone studying image reconstruction and to anyone in PDEs trying to see what kinds of modern applications abound for the subject."
—Mathematical Reviews
"This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters.... The book is written with great care, paying also a lot of attention to the bibliographical and historical notes. It is a recommended reading for all researchers interested in this field."
—Zentralblatt Math
"The goal of this mongraph is to present general existence and uniqueness results for quasilinear parabolic equations whose operator is the subdifferential of a convex Lagrangian which has linear growth. Special emphasis is given to the case of the minimizing total variational flow for which the Neumann, Dirichlet, and Cauchy problem are discussed. The developed techniques apply to problems in continuum mechanics, image restoration and faceted crystal growth."
---Monatshefte für Mathematik
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