Titlebook: Dispersive Equations and Nonlinear Waves; Generalized Korteweg Herbert Koch,Daniel Tataru,Monica Vişan Textbook 2014 Springer Basel 2014 Fo

harmony

https://doi.org/10.1007/978-1-349-19143-7We first review the linear Laplace equation. For functions . we define the Lagrangian . with the Einstein summation convention.

漂白

Matrimony

证实

Stationary phase and dispersive estimatesWe begin with the evaluations of several integrals. Let .. be the .-dimensional Lebesgue measure and define

淡紫色花

Goblet-Cells

Appendix A: Young’s inequality and interpolationYoung’s inequality bounds convolutions in Lebesgue spaces. It is part of the statement that the integral exists for almost all arguments of the convolution. Let .. denote the .-dimensional Lebesgue measure.

诙谐

Appendix B: Bessel functionsThe Bessel functions are confluent hypergeometric functions. They are solutions to confluent hypergeometric differential equations. Here is a very brief introduction.

STAT

Appendic C: The Fourier transformLet . be an integrable complex-valued function. We define its Fourier transform by

incision

迷住

Geometric pde’sWe first review the linear Laplace equation. For functions . we define the Lagrangian . with the Einstein summation convention.