Presentation of the Mumford-Shah Functional -- Functions in the Sobolev Spaces W1,p -- Regularity Properties for Quasiminimizers -- Limits of Almost-Minimizers -- Pieces of C1 Curves for Almost-Minimizers -- Global Mumford-Shah Minimizers in the Plane -- Applications to Almost-Minimizers (n = 2) -- Quasi- and Almost-Minimizers in Higher Dimensions -- Boundary Regularity.Award-winning monograph …
Calculus for Functions of One Variable -- Prerequisites -- Limits and Continuity of Functions -- Differentiability -- Characteristic Properties of Differentiable Functions. Differential Equations -- The Banach Fixed Point Theorem. The Concept of Banach Space -- Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli -- Integrals and…
Dynamique qualitative et théorie des oscillations -- La théorie de la stabilité -- La théorie des bifurcations -- La théorie classique des perturbations et les perturbations singulières -- Systèmes d’oscillateurs couplés -- Solutions ondes stationnaires et systèmes dynamiques -- Electrophysiologie, synchronisation et oscillations en salves.Par sa nature pluridisciplinaire, ce livre s…
Control of Systems Described by Elliptic-Type Partial-Differential Equations under Conjugation Conditions -- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation under Conjugation Conditions -- Control of a System Described by a One-Dimensional Quartic Equation under Conjugation Conditions -- Control of a System Described by a Two-Dimensional …
Preliminary general material -- Steady-State Problems -- Pseudomonotone or weakly continuous mappings -- Accretive mappings -- Potential problems: smooth case -- Nonsmooth problems; variational inequalities -- Systems of equations: particular examples -- Evolution Problems -- Special auxiliary tools -- Evolution by pseudomonotone or weakly continuous mappings -- Evolution governed by accretive …
Bounded Imaginary Powers and H?-Calculus of the Stokes Operator in Unbounded Domains -- Exact Estimates of Solutions to the Robin Boundary Value Problem for Elliptic Non-divergent Second-order Equations in a Neighborhood of the Boundary Conical Point -- Well-posedness of a Two-phase Flow with Soluble Surfactant -- Resolvent Differences for General Obstacles -- Special Finite Time Extinction in …
Wave Maps and Ill-posedness of their Cauchy Problem -- On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations -- Decay and Global Existence for Nonlinear Wave Equations with Localized Dissipations in General Exterior Domains -- Global Existence in the Cauchy Problem for Nonlinear Wave Equations with Variable Speed of Propagation -- On the Nonlinear Cauchy …
Introduction: Basic Notions and Methods -- Heterogeneous Rod -- Heterogeneous Plate -- Finite Rod Structures -- Lattice Structures -- The Multi-Scale Domain Decomposition.Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these …
Atomistic Models -- Lattice Gas Models and Kinetic Monte Carlo Simulations of Epitaxial Growth -- Cluster Diffusion and Island Formation on fcc(111) Metal Surfaces Studied by Atomic Scale Computer Simulations -- A Multiscale Study of the Epitaxial CVD of Si from Chlorosilanes -- Off-lattice Kinetic Monte Carlo Simulations of Strained Heteroepitaxial Growth -- Quasicontinuum Monte Carlo Simulati…
Nonlinear Inverse Problems: Theoretical Aspects and Some Industrial Applications -- Numerical Methods for the Simulation of Incompressible Viscous Flow: An Introduction -- Computational Techniques for the Verification and Control of Hybrid Systems -- Data Assimilation Methods for an Oceanographic Problem -- Ant Colonies: a Nature inspired Paradigm for the Mathematical Modelling of Self-Organizi…