دانلود کتاب Regularity theory and stochastic flows for parabolic SPDEs

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Couverture Introduction to the Series Preface 1 Introduction 2 Stochastic Flows: Preliminary Comments 2.1 Regular Versions of Random Fields 2.2 Comments on the Literature 3 Preliminaries on Well-Posedness and Function Spaces 3 .1 Notations 3.2 Basic Abstract Well-Posedness Theorem 3.3 Basic Particular Case 3.4 An Extension 3.5 Hilbert Scales and Jnterpolation of Random Field Spaces 4 Regularity in Bounded Domains: Some Counterexamples 5 Regularity Theory for Homogeneous Problems 5.1 Abstract Regularity Theory 5.2 Application to Equations in Rd 5.3 Application to Second Order Equations in Bounded Domains: Dirichlet Boundary Condition 5.3.1 L²(D)-Solutions 5.3.2 H¹(D)-Solutions 5.3.3 H²(D)-Solutions 5.3.4 H^n(D)-Solutions, n>=3 5.3.5 H^{-1}(D)-Solutions 5.3.6 H^{-n}(D)-Solutions, n>=2 5.3.7 Summary of Regularity Results for Dirichlet Boundary Value Problem. H^alpha(D)-Solutions, alpha in R 5.3.8 Regularity for the Adjoint Equation 5.4 Application to Equations of Order 2m in Bounded Domains: Dirichlet Boundary Conditions 5.5 Application to Second Order Equations in Bounded Domains: Neumann Boundary Condition 5.5.1 Regularity Results for the Neumann Boundary Value Problem 5.5.2 Regularity for the Adjoint Equation 6 Non-Homogeneous Boundary Value Problems 6.1 General Framework, Standing Assumptions, and Applications 6.2 Preliminaries on Deterministic Boundary Value Problems 6.3 Orientation 6.4 Elementary Regularity 6.5 More Refined Abstract Regularity Results 7 Existence and Regularity of Stochastic Flows 7.1 First Abstract Theorems of Existence and Regularity 7.2 A Pathwise Green Formula 7.3 Transpositions of the Adjoint Flow 7.4 Applications 7.4.1 Dirichlet Boundary Value Problem 7.4.2 Equations of Order 2m with Dirichlet Boundary Conditions 7.4.3 Neumann Boundary Condition 8 An Alternative Approach Acknowledgements References Index