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Field name	Details
Dewey Class	515.353
Title	Parabolic Quasilinear Equations Minimizing Linear Growth Functionals ([EBook]) / by Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles.
Author	Andreu-Vaillo, Fuensanta
Added Personal Name	Mazón, José M.
Added Personal Name	Caselles, Vicent
Other name(s)	SpringerLink (Online service)
Publication	Basel : Birkhäuser , 2004.
Physical Details	XIV, 342 pages : online resource.
Series	Progress in mathematics 0743-1643 ; ; 223
ISBN	9783034879286
Summary Note	Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003. This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi, had a strong influence in the development of variational methods for image denoising and restoration, and pioneered the use of the BV model in image processing. After a full analysis of the model, the minimizing total variation flow is studied under different boundary conditions, and its main qualitative properties are exhibited. In particular, several explicit solutions of the denoising problem are computed.:
Contents note	1 Total Variation Based Image Restoration -- 1.1 Introduction -- 1.2 Equivalence between Constrained and Unconstrained Restoration -- 1.3 The Partial Differential Equation Satisfied by the Minimum of (1.17) -- 1.4 Algorithm and Numerical Experiments -- 1.5 Review of Numerical Methods -- 2 The Neumann Problem for the Total Variation Flow -- 2.1 Introduction -- 2.2 Strong Solutions in L2(?) -- 2.3 The Semigroup Solution in L1(?) -- 2.4 Existence and Uniqueness of Weak Solutions -- 2.5 An LN-L? Regularizing Effect -- 2.6 Asymptotic Behaviour of Solutions -- 2.7 Regularity of the Level Lines -- 3 The Total Variation Flow in ?N -- 3.1 Initial Conditions in L2(?N) -- 3.2 The Notion of Entropy Solution -- 3.3 Uniqueness in Ló(?N) -- 3.4 Existence in Lloc1 -- 3.5 Initial Conditions in L2(?N) -- 3.6 Time Regularity -- 3.7 An LN-L? Regularizing Effect -- 3.8 Measure Initial Conditions -- 4 Asymptotic Behaviour and Qualitative Properties of Solutions -- 4.1 Radially Symmetric Explicit Solutions -- 4.2 Some Qualitative Properties -- 4.3 Asymptotic Behaviour -- 4.4 Evolution of Sets in ?2: The Connected Case -- 4.5 Evolution of Sets in ?2: The Nonconnected Case -- 4.6 Some Examples -- 4.7 Explicit Solutions for the Denoising Problem -- 5 The Dirichlet Problem for the Total Variation Flow -- 5.1 Introduction -- 5.2 Definitions and Preliminary Facts -- 5.3 The Main Result -- 5.4 The Semigroup Solution -- 5.5 Strong Solutions for Data in L2(?) -- 5.6 Existence and Uniqueness for Data in L1(?) -- 5.7 Regularity for Positive Initial Data -- 6 Parabolic Equations Minimizing Linear Growth Functionals: L2-Theory -- 6.1 Introduction -- 6.2 Preliminaries -- 6.3 The Existence and Uniqueness Result -- 6.4 Strong Solution for Data in L2(?)) -- 6.5 Asymptotic Behaviour -- 6.6 Proof of the Approximation Lemma -- 7 Parabolic Equations Minimizing Linear Growth Functionals: L1-Theory -- 7.1 Introduction -- 7.2 The Main Result -- 7.3 The Semigroup Solution -- 7.4 Existence and Uniqueness for Data in L1(?) -- 7.5 A Remark for Strictly Convex Lagrangians -- 7.6 The Cauchy Problem -- A Nonlinear Semigroups -- A.1 Introduction -- A.2 Abstract Cauchy Problem -- A.3 Mild Solutions -- A.4 Accretive Operators -- A.5 Existence and Uniqueness Theorem -- A.6 Regularity of Mild Solutions -- A.7 Completely Accretive Operators -- B Functions of Bounded Variation -- B.2 Approximation by Smooth Functions -- B.3 Traces and Extensions -- B.4 Sets of Finite Perimeter and the Coarea Formula -- B.5 Some Isoperimetric Inequalities -- B.6 The Reduced Boundary -- B.7 Connected Components of Sets of Finite Perimeter -- C Pairings Between Measures and Bounded Functions -- C.1 Trace of the Normal Component of Certain Vector Fields -- Dankwoord/ Acknowledgements.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-0348-7928-6
Links to Related Works	Subject References: Approximation theory . Approximations and Expansions . Calculus of variations . Calculus of variations and optimal control; optimization . Functional Analysis . Partial differential equations . Visualization . Authors: Andreu-Vaillo, Fuensanta . author . Caselles, Vicent . Mazón, José M. . Corporate Authors: SpringerLink (Online service) . Series: Progress in mathematics . Classification: 515.353 . 515.353 (DDC 23) .

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Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

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