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
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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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