Author | Andreu-Vaillo, Fuensanta. author |
---|---|
Title | Parabolic Quasilinear Equations Minimizing Linear Growth Functionals [electronic resource] / by Fuensanta Andreu-Vaillo, Josรฉ M. Mazรณn, Vicent Caselles |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7928-6 |
Descript | XIV, 342 p. online resource |
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 Lรณ(?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