An introduction to Sobolev spaces and interpolation spaces
著者
書誌事項
An introduction to Sobolev spaces and interpolation spaces
（Lecture notes of the Unione matematica italiana, 3）
Springer, c2007
大学図書館所蔵 全44件
注記
"UMI."
Includes bibliographical reference (p. [213]-214) and index
内容説明・目次
内容説明
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.
目次
- 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.Poincare'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.
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