Distributions, Partial Differential Equations, and Harmonic Analysis (Universitext)

Mitrea, Dorina

Springer Nature（2013/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 460 p.
• 言語 ENG
• 商品コード 9781461482079
• DDC分類 515

Full Description

The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.

Contents

Introduction.- Summary of Topological and Functional Analysis Results.- Weak Derivatives.- The Space D0() of Distributions.- The Fourier Transform.- The Space of Tempered Distributions.- Fundamental Solution.- The Laplace Operator.- The Heat Operator.- The Wave Operator.- The Lame Operator.- Fundamental Solutions for Other Operators.- Hypoelliptic operators.- Sobolev spaces.- Appendix.- References.