An Introduction to Sobolev Spaces and Interpolation Spaces

Luc Tartar (auth.)9783540714828, 9783540714835, 3540714820

After publishing an introduction to the Navier–Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.

Table of contents :
Front Matter….Pages I-XXV
Historical Background….Pages 1-7
The Lebesgue Measure, Convolution….Pages 9-14
Smoothing by Convolution….Pages 15-16
Truncation; Radon Measures; Distributions….Pages 17-20
Sobolev Spaces; Multiplication by Smooth Functions….Pages 21-25
Density of Tensor Products; Consequences….Pages 27-31
Extending the Notion of Support….Pages 33-36
Sobolev’s Embedding Theorem, 1 ≤