Advances in Deterministic and Stochastic Analysis

by N. M. Chuong, P. G. Ciarlet, P. Lax, D. Mumford, D. H. Phong

WSP | 2007 | ISBN: 9812705503 9789812705501 9789812770493 | 372 pages | PDF | 13 MB

This volume is dedicated to pure and applied analysis, partial differential equations, geometric analysis and stochastic and infinite-dimensional analysis.

The contributors discuss integral and pseudo-differential operators, which play an important role in partial differential equations, and other methods of solving the partial differential equations, such as the min-max approach to variational problems and boundary value problems.

Contents
Preface
Chapter I: INTEGRAL AND PSEUDODIFFERENTIAL OPERATORS
1. Pseudodifferential Operators of Second Order with Sign-Changed Characteristic Form
2. A Semilinear Nonclassical Pseudodifferential Boundary Value Problem in Sobolev Spaces Hl,p 1 < p < w
3. Singular Integral Operators in Functional Spaces of Morrey Type
4. Classification of Integral Transforms
Chapter II : PARTIAL DIFFERENTIAL EQUATIONS
5. Unified Minimax Methods
6. Some Remarks on Single Conservation Laws
7. Iterative Method for Solving a Mixed Boundary Value Problem for Biharmonic Type Equation
8. Numerical Solution to a Non-Linear Parabolic Boundary Control Problem
9. A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions
10. On the Cauchy Problem for a Quasilinear Weakly Hyperbolic System in Two Variables and Applications to that for Weakly Hyperbolic Classical Monge- Ampkre Equations
11. Some Singular Perturbation Problems Related to the Navier- Stokes Equations
Chapter III : GEOMETRIC ANALYSIS
12. Monotone Invariants and Embeddings of Statistical Manifolds
13. Graded Cech Cohomology in Noncommutative Geometry
14. Sobolev Spaces with Weight on Riemannian Manifolds
Chapter IV : STOCHASTIC AND INFINITE-DIMENTIONAL ANALYSIS
15. Stochastic Population Control and RSDE with Jumps
16. Noncausal Stochastic Calculus Revisited - Around the So-called Ogawa Integral
17. Infinite-Dimensional Stochastic Analysis and Foundations of Quantum Mechanics
18. Noncommutative Trigonometry and Quantum Mechanics with TOC BookMarkLinks