Advances in Harmonic Analysis and Partial Differential Equations -

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Résumé :
Local smoothing of Fourier integral operators and Hermite functions.- On () -classes on the Engel group.- Gelfand triples for the Kohn-Nirenberg quantization on homogeneous Lie groups.- A multiplicity result for a non-homogeneous subelliptic problem with Sobolev exponent.- The Dixmier trace and the noncommutative residue for multipliers on compact manifolds.- On the focusing energy-critical 3D quintic inhomogeneous NLS.- Lifespan of solutions to nonlinear Schr?dinger equations with general homogeneous nonlinearity of the critical order.- Spectral theory for magnetic Schr?dinger operators in exterior domains with exploding and oscillating long-range potentials.- Simple proof of the estimate of solutions to Schr?dinger equations with linear and sub-linear potentials in modulation spaces.- Remark on asymptotic order for the energy critical nonlinear damped wave equation to the linear heat equation via the Strichartz estimates.- On uniqueness for the generalized Choquard equation.- Characterization of the ground state to the intercritical NLS with a linear potential by the virial functional.- Well-posedness for a generalized Klein-Gordon-Schr?dinger equations....

Sommaire:
This book originates from the session Harmonic Analysis and Partial Differential Equations held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers.