close
1.

図書

図書
by Graeme W. Milton
出版情報: Cambridge : Cambridge University Press, c2002  xxviii, 719 p. ; 26 cm
シリーズ名: Cambridge monographs on applied and computational mathematics ; 6
所蔵情報: loading…
2.

図書

図書
Jürgen Jost
出版情報: New York ; Tokyo : Springer, c2002  xi, 325 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 214
所蔵情報: loading…
目次情報: 続きを見る
Introduction
The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
The maximum principle
Existence techniques
methods based on the maximum principle / I:
Parabolic methods / II:
The Head equation
The wave equation and its connections with the Laplace and heat equation
The heat equation, semigroups, and Brownian motion
The Dirichlet principle
Variational methods for the solution of PDE (Existence techniques III)
Sobolev spaces and L2 regularity theory
Strong solutions
The regularity theory of Schauder and the continuity method (Existence techniques IV)
The Moser iteration method and the reqularity theorem of de Giorgi and Nash
Banach and Hilbert spaces
The Lp-spaces
Bibliography
Introduction
The Laplace equation as the prototype of an elliptic partial differential equation of 2nd order
The maximum principle
3.

図書

図書
Giuseppe Da Prato, Jerzy Zabczyk
出版情報: Cambridge : Cambridge University Press, 2002  xvi, 379 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 293
所蔵情報: loading…
目次情報: 続きを見る
Theory in the Space of Continuous Functions / Part I:
Gaussian measures / 1:
Spaces of continuous functions / 2:
Heat equation / 3:
Poisson's equation / 4:
Elliptic equations with variable coefficients / 5:
Ornstein-Uhlenbeck equations / 6:
General parabolic equations / 7:
Parabolic equations in open sets / 8:
Theory in Sobolev Spaces with a Gaussian Measure / Part II:
L2 and Sobolev spaces / 9:
Ornstein-Uhlenbeck semigroups on Lp(H, mu) / 10:
Perturbations of Ornstein-Uhlenbeck semigroups / 11:
Gradient systems / 12:
Applications to Control Theory
Second order Hamilton-Jacobi equations / 13:
Hamilton-Jacobi inclusions / 14:
Theory in the Space of Continuous Functions / Part I:
Gaussian measures / 1:
Spaces of continuous functions / 2:
4.

図書

図書
Andrew Majda
出版情報: New York : Courant Institute of Mathematical Sciences, New York University , Providence, R.I : American Mathematical Society, 2003  ix, 234 p. ; 26 cm
シリーズ名: Courant lecture notes in mathematics ; 9
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introduction / Chapter 1.:
Basic Properties of the Equations with Rotation and Stratification / 1.1.:
Two-Dimensional Exact Solutions / 1.2.:
Buoyancy and Stratification / 1.3.:
Jet Flows with Rotation and Stratification / 1.4.:
From Vertical Stratification to Shallow Water / 1.5.:
Some Remarkable Features of Stratified Flow / Chapter 2.:
Energy Principle / 2.1.:
Vorticity in Stratified Fluids and Exact Solutions Motivated by Local Analysis / 2.2.:
Use of Theorem 2.4: Exact Two-Dimensional Solutions / 2.3.:
Nonlinear Plane Waves in Stratified Flow: Internal Gravity Waves / 2.4.:
Exact Solutions with Large-Scale Motion and Nonlinear Plane Waves / 2.5.:
More Details for Theorem 2.7 on Special Exact Solutions for the Boussinesq Equations Including Plane Waves / 2.6.:
Linear and Nonlinear Instability of Stratified Flows with Strong Stratification / Chapter 3.:
Boussinesq Equations and Vorticity Stream Formulation / 3.1.:
Nonlinear Instability of Stratified Flows / 3.2.:
Shear Flows / 3.3.:
Some Background Facts on ODEs / 3.4.:
Rotating Shallow Water Theory / Chapter 4.:
Rotating Shallow Water Equations / 4.1.:
Conservation of Potential Vorticity / 4.2.:
Nonlinear Conservation of Energy / 4.3.:
Linear Theory for the Rotating Shallow Water Equations / 4.4.:
Nondimensional Form of the Rotating Shallow Water Equations / 4.5.:
Derivation of the Quasi-Geostrophic Equations / 4.6.:
The Quasi-Geostrophic Equations as a Singular PDE Limit / 4.7.:
The Model Rotating Shallow Water Equations / 4.8.:
Preliminary Mathematical Considerations / 4.9.:
Regorous Convergence of the Model Rotating Shallow Water Equations to the Quasi-Geostrophic Equations / 4.10.:
Proof of the Convergence Theorem / 4.11.:
Linear and Weakly Nonlinear Theory of Dispersive Waves with Geophysical Examples / Chapter 5.:
Linear Wave Midlatitude Planetary Equations / 5.1.:
Dispersive Waves: General Properties / 5.2.:
Interpretation of Group Velocity / 5.3.:
Distant Propagation from a Localized Source / 5.4.:
WKB Methods for Linear Dispersive Waves / 5.5.:
Beyond Caustics: Eikonal Equation Revisited / 5.6.:
Weakly Nonlinear WKB for Perturbations Around a Constant State / 5.7.:
Nonlinear WKB and the Boussinesq Equations / 5.8.:
Simplified Equations for the Dynamics of Strongly Stratified Flow / Chapter 6.:
Nondimensionalization of the Boussinesq Equations for Stably Stratified Flow / 6.1.:
The Vorticity Stream Formulation and Elementary Properties of the Limit Equations for Strongly Stratified Flow / 6.2.:
Solutions of the Limit Dynamics with Strong Stratification as Models for Laboratory Experiments / 6.3.:
The Stratified Quasi-Geostrophic Equations as a Singular Limit of the Rotating Boussinesq Equations / Chapter 7.:
The Rotating Boussinesq Equations / 7.1.:
The Nondimensional Rotating Boussinesq Equations / 7.3.:
Formal Asymptotic Derivation of the Quasi-Geostrophic Equations as a Distinguished Asymptotic Limit of Small Rossby and Froude Numbers / 7.4.:
Rigorous Convergence of the Rotating Boussinesq Equations to the Quasi-Geostrophic Equations / 7.5.:
Introduction to Averaging over Fast Waves for Geophysical Flows / 7.6.:
Motivation for Fast-Wave Averaging / 8.1.:
A General Framework for Averaging over Fast Waves / 8.3.:
Elementary Analytic Models for Comparing Instabilities at Low Froude Numbers with the Low Froude Number Limit Dynamics / 8.4.:
The Rapidly Rotating Shallow Water Equations with Unbalanced Initial Data in the Quasi-Geostrophic Limit / 8.5.:
The Interaction of Fast Waves and Slow Dynamics in the Rotating Stratified Boussinesq Equations / 8.6.:
Waves and PDEs for the Equatorial Atmosphere and Ocean / Chapter 9.:
Introduction to Equatorial Waves for Rotating Shallow Water / 9.1.:
The Equatorial Primitive Equations / 9.2.:
The Nonlinear Equatorial Long-Wave Equations / 9.3.:
A Simple Model for the Steady Circulation of the Equatorial Atmosphere / 9.4.:
Bibliography
Preface
Introduction / Chapter 1.:
Basic Properties of the Equations with Rotation and Stratification / 1.1.:
5.

図書

図書
V. Lakshmikantham and S. Köksal
出版情報: London : Taylor & Francis, c2003  x, 318 p. ; 26 cm
シリーズ名: Series in mathematical analysis and applications / Edited by Ravi P. Agarwal and Donal O'Regan ; v. 7
所蔵情報: loading…
6.

図書

図書
Ovidiu Calin, Der-Chen Chang
出版情報: Boston : Birkhäuser, c2005  xv, 278 p. ; 24 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
所蔵情報: loading…
目次情報: 続きを見る
Preface
Introductory Chapter
Laplace Operator 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
Mechanical Curves
Bibliography
Index
Preface
Introductory Chapter
Laplace Operator on Riemannian Manifolds
7.

図書

図書
Dan Henry ; with editorial assistance from Jack Hale and Antônio Luiz Pereira
出版情報: New York : Cambridge University Press, 2005  viii, 206 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 318
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Geometrical preliminaries / 1:
Differential calculus of boundary perturbations / 2:
Examples using the implicit function theorem / 3:
Bifurcation problems / 4:
The transversality theorem / 5:
Generic perturbation of the boundary / 6:
Boundary operators for second-order elliptic equations / 7:
The method of rapidly-oscillating solutions / 8:
Introduction
Geometrical preliminaries / 1:
Differential calculus of boundary perturbations / 2:
8.

図書

図書
Luca Capogna, Carlos E. Kenig, Loredana Lanzani
出版情報: Providence, R.I. : American Mathematical Society, c2005  x, 155 p. ; 26 cm
シリーズ名: University lecture series ; 35
所蔵情報: loading…
目次情報: 続きを見る
Motivation and statement of the main results
The relation between potential theory and geometry for planar domains
Preliminary results in potential theory
Reifenberg flat and chord arc domains
Further results on Reifenberg flat and chord arc domains
From the geometry of a domain to its potential theory
From potential theory to the geometry of a domain
Higher codimension and further regularity results
Bibliography
Motivation and statement of the main results
The relation between potential theory and geometry for planar domains
Preliminary results in potential theory
9.

図書

図書
Guy David
出版情報: Basel : Birkhäuser, c2005  xiv, 581 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 233
所蔵情報: loading…
目次情報: 続きを見る
Foreword
Presentation of the Mumford-Shah functional
Functions in the Sobolev spaces
Regularity properties for quasiminimizers
Limits of almost-minimizers
Pieces of C^1 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
Foreword
Presentation of the Mumford-Shah functional
Functions in the Sobolev spaces
10.

図書

図書
Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
出版情報: Heidelberg : Springer, c2011  xv, 523 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 343
所蔵情報: loading…
目次情報: 続きを見る
Basic Analysis / 1:
Basic Real Anslysis / 1.1:
Holder and Convolution Inequslities / 1.1.1:
The Atomic Decomposition / 1.1.2:
Proof of Refined Young Inequslityp8 / 1.1.3:
A Bilinear Interpolation Theorem / 1.1.4:
A Linear Interpolation Result / 1.1.5:
The Hardy-Littlewood Maximal Function / 1.1.6:
The Fourier Transform / 1.2:
Fourier Transforms of Functions and the Schwartz Space / 1.2.1:
Tempered Distributions and the Fourier Transform / 1.2.2:
A Few Calculations of Fourier Transforms / 1.2.3:
Homogeneous Sobolev Spaces / 1.3:
Definition and Basic Properties / 1.3.1:
Sobolev Embedding in Lebesgue Spaces / 1.3.2:
The Limit Case Hd/2 / 1.3.3:
The Embedding Theorem in Hölder Spaces / 1.3.4:
Nonhomogeneous Sobolev Spaces on Rd / 1.4:
Embedding / 1.4.1:
A Density Theorem / 1.4.3:
Hardy Inequality / 1.4.4:
References and Remarks / 1.5:
Littlewood-Paley Theory / 2:
Functions with Compactly Supported Fourier Transforms / 2.1:
Bernstein-Type Lemmas / 2.1.1:
The Smoothing Effect of Heat Flow / 2.1.2:
The Action of a Diffeomorphism / 2.1.3:
The Effects of Some Nonlinear Functions / 2.1.4:
Dyadic Partition of Unity / 2.2:
Homogeneous Besov Spaces / 2.3:
Characterizations of Homogeneous Besov Spaces / 2.4:
Besov Spaces, Lebesgue Spaces, and Refined Inequalities / 2.5:
Homogeneous Paradifferential Calculus / 2.6:
Homogeneous Bony Decomposition / 2.6.1:
Action of Smooth Functions / 2.6.2:
Time-Space Besov Spaces / 2.6.3:
Nonhomogeneous Besov Spaces / 2.7:
Nonhomogeneous Paradifferential Calculus / 2.8:
The Bony Decomposition / 2.8.1:
The Paralinearization Theorem / 2.8.2:
Besov Spaces and Compact Embeddings / 2.9:
Commutator Estimates / 2.10:
Around the Space B&infty;,&infty;1 / 2.11:
Transport and Transport-Diffusion Equations / 2.12:
Ordinary Differential Equations / 3.1:
The Cauchy-Lipschitz Theorem Revisited / 3.1.1:
Estimates for the Flow / 3.1.2:
A Blow-up Criterion for Ordinary Differential Equations / 3.1.3:
Transport Equations: The Lipschitz Case / 3.2:
A Priori Estimates in General Besov Spaces / 3.2.1:
Refined Estimates in Besov Spaces with Index 0 / 3.2.2:
Solving the Transport Equation in Besov Spaces / 3.2.3:
Application to a Shallow Water Equation / 3.2.4:
Losing Estimates for Transport Equations / 3.3:
Linear Loss of Regularity in Besov Spaces / 3.3.1:
The Exponential Loss / 3.3.2:
Limited Loss of Regularity / 3.3.3:
A Few Applications / 3.3.4:
Transport-Diffusion Equations / 3.4:
A Priori Estimates / 3.4.1:
Exponential Decay / 3.4.2:
Quasilinear Symmetric Systems / 3.5:
Definition and Examples / 4.1:
Linear Symmetric Systems / 4.2:
The Well-posedness of Linear Symmetric Systems / 4.2.1:
Finite Propagation Speed / 4.2.2:
Further Well-posedness Results for Linear Symmetric Systems / 4.2.3:
The Resolution of Quasilinear Symmetric Systems / 4.3:
Paralinearization and Energy Estimates / 4.3.1:
Convergence of the Scheme / 4.3.2:
Completion of the Proof of Existence / 4.3.3:
Uniqueness and Continuation Criterion / 4.3.4:
Data with Critical Regularity and Blow-up Criteria / 4.4:
Critical Besov Regularity / 4.4.1:
A Refined Blow-up Crndition / 4.4.2:
Continuity of the Flow Map / 4.5:
The Incompressible Navier-Stokes System / 4.6:
Basic Facts Concerning the Navier-Stokes System / 5.1:
Well-posedness in Sobolev Spaces / 5.2:
A General Result / 5.2.1:
The Behavior of the Hd/2-1 Norm Near 0 / 5.2.2:
Results Related to the Structure of the System / 5.3:
The Particular Case of Dimension Two / 5.3.1:
The Case of Dimension Three / 5.3.2:
An Elementary Lp Approach / 5.4:
The Endpoint Space for Picard's Scheme / 5.5:
The Use of the L1-smoothing Effect of the Heat Flow / 5.6:
The Cannone-Meyer-Planchon Theorem Revisited / 5.6.1:
The Flow of the Solutions of the Navier-Stokes System / 5.6.2:
Anisotropic Viscosity / 5.7:
The Case of L2 Data with One Vertical Derivative in L2 / 6.1:
A Global Existence Result in Anisotropic Besov Spaces / 6.2:
Anisotropic Localization in Fourier Space / 6.2.1:
The Functional Framework / 6.2.2:
Statement of the Main Result / 6.2.3:
Some Technical Lemmas / 6.2.4:
The Proof of Existence / 6.3:
The Proof of Uniqueness / 6.4:
Euler System for Perfect Incompressible Fluids / 6.5:
Local Well-posedness Results for Inviscid Fluids / 7.1:
The Biot-Savart Law / 7.1.1:
Estimates for the Pressure / 7.1.2:
Another Formulation of the Euler System / 7.1.3:
Local Existence of Smooth Solutions / 7.1.4:
Uniqueness / 7.1.5:
Continuation Criteria / 7.1.6:
Global Existence Results in Dimension Two / 7.2:
Smooth Solutions / 7.2.1:
The Borderline Case / 7.2.2:
The Yudovich Theorem / 7.2.3:
The Inviscid Limit / 7.3:
Regularity Results for the Navier-Stokes System / 7.3.1:
The Smooth Case / 7.3.2:
The Rough Case / 7.3.3:
Viscous Vortex Patches / 7.4:
Results Related to Striated Regularity / 7.4.1:
A Stationary Estimate for the Velocity Field / 7.4.2:
Uniform Estimates for Striated Regularity / 7.4.3:
A Global Convergence Result for Striated Regularity / 7.4.4:
Application to Smooth Vortex Patches / 7.4.5:
Strichartz Estimates and Applications to Semilinear Dispersive Equations / 7.5:
Examples of Dispersive Estimates / 8.1:
The Dispersive Estimate for the Free Transport Equation / 8.1.1:
The Dispersive Estimates for the Schrdillger Equation / 8.1.2:
Integral of Oscillating Functions / 8.1.3:
Dispersive Estimates for the Wave Equation / 8.1.4:
The L2 Boundedness of Some Fourier Integral Operators / 8.1.5:
Billnear Methods / 8.2:
The Duality Method and the TT* Argument / 8.2.1:
Strichartz Estimates: The Case q > 2 / 8.2.2:
Strichartz Estimates: The Endpoint Case q = 2 / 8.2.3:
Application to the Cubic Semilinear Schrödinger Equation / 8.2.4:
Strichartz Estimates for the Wave Equation / 8.3:
The Basic Strichartz Estimate / 8.3.1:
The Refined Strichartz Estimate / 8.3.2:
The Qulntic Wave Equation in R3 / 8.4:
The Cubic Wave Equation in R3 / 8.5:
Solutions in H1 / 8.5.1:
Local and Global Well-posedness for Rough Data / 8.5.2:
The Nonlinear Interpolation Method / 8.5.3:
Application to a Class of Semilinear Wave Equations / 8.6:
Smoothing Effect in Quasilinear Wave Equations / 8.7:
A Well-posedness Result Based on an Energy Method / 9.1:
The Main Statement and the Strategy of its Proof / 9.2:
Refined Paralinearization of the Wave Equation / 9.3:
Reduction to a Microlocal Strichartz Estimate / 9.4:
Microlocal Strichartz Estimates / 9.5:
A Rather General Statement / 9.5.1:
Geometrical Optics / 9.5.2:
The Solution of the Eikonal Equation / 9.5.3:
The Transport Equation / 9.5.4:
The Approximation Theorem / 9.5.5:
The Proof of Theorem 9.16 / 9.5.6:
The Compressible Navier-Stokes System / 9.6:
About the Model / 10.1:
General Overview / 10.1.1:
The Barotropic Navier-Stokes Equations / 10.1.2:
Local Theory for Data with Critical Regularity / 10.2:
Scaling Invariance and Statement of the Main Result / 10.2.1:
Existence of a Local Solution / 10.2.2:
A Continuation Criterion / 10.2.4:
Local Theory for Data Bounded Away from the Vacuum / 10.3:
A Priori Estimates for the Linearized Momentum Equation / 10.3.1:
Global Existence for Small Data / 10.3.2:
Statement of the Results / 10.4.1:
A Spectral Analysis of the Linearized Equation / 10.4.2:
A Prioli Estimates for the Linearized Equation / 10.4.3:
Proof of Global Existence / 10.4.4:
The Incompressible Limit / 10.5:
Main Results / 10.5.1:
The Case of Small Data with Critical Regularity / 10.5.2:
The Case of Large Data with More Regularity / 10.5.3:
References / 10.6:
List of Notations
Index
Basic Analysis / 1:
Basic Real Anslysis / 1.1:
Holder and Convolution Inequslities / 1.1.1:
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼