Intro
Preface
Introduction
Contents
Acronyms
1 Nonlinear Diffusion Equations with Slow and Fast Diffusion
1.1 A Continuous Potential with a Polynomial Growth
1.1.1 Functional Framework and Preliminaries
1.1.2 The Minimization Problem
1.1.3 Main Results for the Slow Diffusion Case
1.2 A Free Boundary Problem for a Special Fast Diffusion Case
2 Weakly Coercive Nonlinear Diffusion Equations
2.1 Problem Presentation
2.2 Functional Setting and the Minimization Problem
2.3 A Time and Space Dependent Potential
2.4 A Time Dependent Potential

3 Nonlinear Diffusion Equations with a Noncoercive Potential
3.1 Problem Statement and the Functional Framework
3.2 The Minimization Problem
3.3 Main Results for the Noncoercive Case
3.4 Existence in a Self-organized Criticality (SOC) Model
4 Nonlinear Parabolic Equations in Divergence Form with Wentzell Boundary Conditions
4.1 Problem Presentation
4.2 The Strongly Coercive Case
4.3 The Weakly Coercive Case
4.4 The Semigroup Approach
4.4.1 The Obstacle Problem
4.4.2 The Total Variation Wentzell Flow
5 A Nonlinear Control Problem in Image Denoising

6.4.3 Optimality Conditions for (P)
7 Appendix
7.1 Lp Spaces, Sobolev Spaces, and Vectorial Spaces
7.2 Operators in Banach Spaces
7.3 Convex Functions and Subdifferential Mappings
References
Index