Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups -- The Heat Kernel and Frequency Localized Functions on the Heisenberg Group -- A Generalization of the Rudin#x2013;Carleson Theorem -- Evolution Equations and Generalized Fourier Integral Operators -- The Solvability and Subellipticity of Systems of Pseudodifferential Operators -- Uniform Exponential Decay for Viscous Damped Systems#x002A; -- The Hyperbolic Symmetrizer: Theory and Applications -- Time Global Solutions to the Cauchy Problem for Multidimensional Kirchhoff Equations -- The Order of Accuracy of Quadrature Formulae for Periodic Functions -- A Note on the Oseen Kernels -- Instability Behavior and Loss of Regularity -- Decay Estimates for Variable Coefficient Wave Equations in Exterior Domains -- On Gevrey Well-Posedness of the Cauchy Problem for Some Noneffectively Hyperbolic Operators -- Singularities of the Scattering Kernel Related to Trapping Rays -- Analytic Hypoellipticity for a Sum of Squares of Vector Fields in #x211D; Whose Poisson Stratification Consists of a Single Symplectic Stratum of Codimension Four -- Multidimensional Soliton Integrodifferential Systems -- Selected lectures in Microlocal Analysis.

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.