1.Historical background.- 2.The Lebesgue measure, convolution.- 3.Smoothing by convolution.- 4.Truncation, Radon measures, distributions.- 5.Sobolev spaces, multiplication by smooth functions.- 6.Density of tensor products, consequences.- 7.Extending the notion of support.- 8.Sobolev’s embedding theorem, 1 \leq p < N.- 9.Sobolev’s embedding theorem, N \leq p \leq \infty.- 10.Poincae’s inequality.-11.The equivalence lemma, compact embeddings.- 12.Regularity of the boundary, consequences.- 13.Traces on the boundary.- 14.Green’s formula.-15.The Fourier transform.- 16.Traces of Hs(RN).- 17.Proving that a point is too small.- 18.Compact embeddings.- 19.Lax–Milgram lemma.- 20.The space H(div; \Omega).- 21.Background on interpolation, the complex method.- 22.Real interpolation: K-method.- 23.Interpolation of L2 spaces with weights.- 24.Real interpolation: J-method.- 25.Interpolation inequalities, the spaces (E0,E1)\theta,1.- 26.The Lions–Peetre reiteration theorem.- 27.Maximal functions.- 28.Bilinear and nonlinear interpolation.- 29.Obtaining Lp by interpolation, with the exact norm.- 30.My approach to Sobolev’s embedding theorem.- 31.My generalization of Sobolev’s embedding theorem.- 32.Sobolev’s embedding theorem for Besov spaces.- 33.The Lions–Magenes space H001/2(\Omega ).- 34.Defining Sobolev spaces and Besov spaces for \Omega.- 35.Characterization of Ws,p(RN).- 36.Characterization of Ws,p (\Omega).- 37.Variants with BV spaces.- 38.Replacing BV by interpolation spaces.- 39.Shocks for quasi-linear hyperbolic systems.- 40.Interpolation spaces as trace spaces.- 41.Duality and compactness for interpolation spaces.- 42.Miscellaneous questions.- 43.Biographical information.- 44.Abbreviations and mathematical notation.- References.- Index.
An Introduction to Sobolev Spaces and Interpolation Spaces / Edition 1by Luc Tartar
Pub. Date: 07/20/2007
Publisher: Springer Berlin Heidelberg
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
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.
- Springer Berlin Heidelberg
- Publication date:
- Lecture Notes of the Unione Matematica Italiana Series , #3
- Edition description:
- Product dimensions:
- 9.21(w) x 6.14(h) x 0.52(d)
Table of Contents
Most Helpful Customer Reviews
See all customer reviews