Selected topics in partial differential equations Claude Zuily

Format:

Book

Author/Creator:

Zuily, Claude, 1945- author.

Series:

Universitext

Universitext 2191-6675

Language:

English

Subjects (All):

Differential equations, Partial.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Springer [2026]

Summary:

"This book presents a collection of topics in partial differential equations designed to serve as a bridge to research for Master's students. Drawing on material originally developed for student projects, the selected topics require only standard prerequisites such as differential calculus, complex analysis, Fourier analysis, the Lebesgue integral, and some functional analysis. They span a broad range of problems in PDE, including Burgers’ equation, the wave equation, spectral theory of the Laplacian, and harmonic functions. The topics and their presentation are intended to help readers access the research literature. Offering a diverse set of themes that highlights the richness of the field and opens the door to research, this book will be of interest to graduate students studying PDEs. With original material closely related to the author’s own research, it can also serve as a concise reference for researchers"-- Springer Nature Link

Contents:

The method of characteristics

Cauchy-Kovalevski theorem

The method of stationary phase

Continuity of nonlinear maps on Sobolev and Lebesgue spaces

The Burgers equation

Mathematical analysis of surface waves

Continuity of the Dirichlet-Neumann operator

Spectral theory of the Laplacian on the sphere and on the torus

The hydrogen atom

Spectral theory of the Dirichlet problem for the Laplacian

Weyl’s law

Almgren’s theory, unique continuation and Hausdorff measure of nodal sets of harmonic functions

Nodal domains of eigenfunctions of the Laplacian

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Springer Nature Link, viewed July 7, 2026)

Other Format:

Print version Zuily, Claude, 1945- Selected topics in partial differential equations

ISBN:

9783032240828

3032240824

OCLC:

1601944251

Access Restriction:

Restricted for use by site license