Linearization -- Fixed-Point Theorems -- Degree Theory and Applications -- Minimization Methods -- Topological and Variational Methods.Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered thr…
Basic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounde…
Three-Dimensional Differential Geometry -- Differential Geometry of Surfaces -- Applications to Three-Dimensional Elasticity in Curvilinear Coordinates -- Applications to Shell Theory.curvilinear coordinates. This treatment includes in particular a direct proof of the three-dimensional Korn inequality in curvilinear coordinates. The fourth and last chapter, which heavily relies on Chapter 2, be…
This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup ran…
Setting the Scene -- Two-Point Boundary Value Problems -- The Heat Equation -- Finite Difference Schemes for the Heat Equation -- The Wave Equation -- Maximum Principles -- Poisson's Equation in Two Space Dimensions -- Orthogonality and General Fourier Series -- Convergence of Fourier Series -- The Heat Equation Revisited -- Reaction-Diffusion Equations -- Applications of the Fourier Transform.…
Kohn's Proof of the Hypoellipticity of the Hörmander Operators -- Compactness Criteria for the Resolvent of Schrödinger Operators -- Global Pseudo-differential Calculus -- Analysis of some Fokker-Planck Operator -- Return to Equillibrium for the Fokker-Planck Operator -- Hypoellipticity and Nilpotent Groups -- Maximal Hypoellipticity for Polynomial of Vector Fields and Spectral Byproducts -- …
Balance Laws -- to Continuum Physics -- Hyperbolic Systems of Balance Laws -- The Cauchy Problem -- Entropy and the Stability of Classical Solutions -- The L1 Theory for Scalar Conservation Laws -- Hyperbolic Systems of Balance Laws in One-Space Dimension -- Admissible Shocks -- Admissible Wave Fans and the Riemann Problem -- Generalized Characteristics. -- Genuinely Nonlinear Scalar Conservati…
Homological Methods in Fixed Point Theory -- Coincidence Theory -- On the Lefschetz Fixed Point Theorem -- Linearizations for Maps of Nilmanifolds and Solvmanifolds -- Homotopy Minimal Periods -- Periodic Points and Braid Theory -- Fixed Point Theory of Multivalued Weighted Maps -- Fixed Point Theory for Homogeneous Spaces A Brief Survey -- Equivariant Fixed Point Theory -- A Note on Equivarian…
A. Giorgilli: Preface -- G. Benettin: Physical Applications of Nekhoroshev Theorem and Exponential Estimates -- J. Henrard: The Adiabatic Invariant Theory and Applications -- S. Kuksin: Lectures on Hamiltonian Methods in Nonlinear PDEs.This volume collects three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim …
Introductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators …