This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations.
Key topics include:
* Operators as "sums of squares" of real and complex vector fields: both analytic hypoellipticity and regularity for very low regularity coefficients;
* Nonlinear evolution equations: Navier–Stokes system, Strichartz estimates for the wave equation, instability and the Zakharov equation and eikonals;
* Local solvability: its connection with subellipticity, local solvability for systems of vector fields in Gevrey classes;
* Hyperbolic equations: the Cauchy problem and multiple characteristics, both positive and negative results.
Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.
List of contributors:
L. Ambrosio N. Lerner
H. Bahouri X. Lu
S. Berhanu J. Metcalfe
J.-M. Bony T. Nishitani
N. Dencker V. Petkov
S. Ervedoza J. Rauch
I. Gallagher M. Reissig
J. Hounie L. Stoyanov
E. Jannelli D. S. Tartakoff
K. Kajitani D. Tataru
A. Kurganov F. Treves
G. Zampieri
E. Zuazua
Author(s): Luigi Ambrosio (auth.), Antonio Bove, Daniele Del Santo, M.K. Venkatesha Murthy (eds.)
Series: Progress in Nonlinear Differential Equations and Their Applications 78
Edition: 1
Publisher: Birkhäuser Basel
Year: 2009
Language: English
Pages: 292
Tags: Partial Differential Equations;Dynamical Systems and Ergodic Theory;Mathematical Methods in Physics;Applications of Mathematics;Ordinary Differential Equations;Analysis
Front Matter....Pages i-xiv
Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups....Pages 1-16
The Heat Kernel and Frequency Localized Functions on the Heisenberg Group....Pages 17-35
A Generalization of the Rudin–Carleson Theorem....Pages 37-57
Evolution Equations and Generalized Fourier Integral Operators....Pages 59-72
The Solvability and Subellipticity of Systems of Pseudodifferential Operators....Pages 73-94
Uniform Exponential Decay for Viscous Damped Systems*....Pages 95-112
The Hyperbolic Symmetrizer: Theory and Applications....Pages 113-139
Time Global Solutions to the Cauchy Problem for Multidimensional Kirchhoff Equations....Pages 141-153
The Order of Accuracy of Quadrature Formulae for Periodic Functions....Pages 155-159
A Note on the Oseen Kernels....Pages 161-170
Instability Behavior and Loss of Regularity....Pages 171-200
Decay Estimates for Variable Coefficient Wave Equations in Exterior Domains....Pages 201-216
On Gevrey Well-Posedness of the Cauchy Problem for Some Noneffectively Hyperbolic Operators....Pages 217-233
Singularities of the Scattering Kernel Related to Trapping Rays....Pages 235-251
Analytic Hypoellipticity for a Sum of Squares of Vector Fields in ℝ 3 Whose Poisson Stratification Consists of a Single Symplectic Stratum of Codimension Four....Pages 253-261
Multidimensional Soliton Integrodifferential Systems....Pages 263-289
Selected lectures in Microlocal Analysis....Pages 291-301
