Mitrea D. Diistributions, Partial Differential Equations, and Harmonic Analysis

N.-Y.: Springer, 2013. - 460p.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.​Weak Derivatives
The Space $$\mathcal{D}^{\prime}(\Omega )$$ of Distributions
The Schwartz Space and the Fourier Transform
The Space of Tempered Distributions
The Concept of a Fundamental Solution
Hypoelliptic Operators
The Laplacian and Related Operators
The Heat Operator and Related Versions
The Wave Operator
The Lamé and Stokes Operators
More on Fundamental Solutions for Systems
Solutions to Selected Exercises
Appendix