An Introduction to Sobolev Spaces and Interpolation Spaces [Paperback]

After publishing an introduction to the NavierStokes 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.

After publishing an introduction to the NavierStokes 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.

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.Sobolevs embedding theorem, 1 \leq p < N.- 9.Sobolevs embedding theorem, N \leq p \leq \infty.- 10.Poincar?es inequality.-11.The equivalence lemma, compact embeddings.- 12.Regularity of the boundary, consequences.- 13.Traces on the boundary.- 14.Greens formula.-15.The Fourier transform.- 16.Traces of Hs(RN).- 17.Proving that a point is too small.- 18.Compact embeddings.- 19.LaxMilgram 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 LionsPeetre reiteration theorem.- 27.Maximal functions.- 28.Bilinear and nonlinear interpolation.- 29.Obtaining Lp by interpolation, with the exact norm.- 30.My approach to Sobolevs embedding theorem.- 31.My generalization of Sobolevs embedding theorem.- 32.Sobolevslc*