An Introduction to Sobolev Spaces and Interpolation SpacesSpringer Science & Business Media, 26 mai 2007 - 219 pages 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 des matières
Historical Background | 1 |
Density of Tensor Products Consequences | 26 |
8 | 36 |
Sobolevs Embedding Theorem N p | 42 |
The Equivalence Lemma Compact Embeddings | 52 |
Traces on the Boundary | 64 |
LaxMilgram Lemma | 68 |
The Fourier Transform | 73 |
Interpolation Inequalities the Spaces Eo E101 | 123 |
Maximal Functions | 130 |
Obtaining LP by Interpolation with the Exact Norm | 144 |
Sobolevs Embedding Theorem for Besov Spaces | 155 |
Defining Sobolev Spaces and Besov Spaces | 162 |
Characterization of W8P | 173 |
Shocks for QuasiLinear Hyperbolic Systems | 182 |
Interpolation Spaces as Trace Spaces | 191 |
The Space Hdiv | 78 |
Traces of HsRN | 83 |
Background on Interpolation the Complex Method | 102 |
Interpolation of L² Spaces with Weights | 117 |
Biographical Information 205 | 204 |
217 | |
Expressions et termes fréquents
American mathematician argument ball Banach space belongs Besov space bounded open set continuous functions converges decomposition deduces defined Definition denotes dense derivatives distributions dual dx dy Eon E1 equation equivalent norms exists extends Əxj finite formula Fourier transform function f gives grad(u H(div H¹(N H¹(R H¹(RN H³ RN Hardy's inequality Hilbert Hölder Hölder's inequality implies integral interpolation spaces Jaak PEETRE Jacques-Louis LIONS K-method L¹(N L¹(R L¹(RN L²(N L²(RN Laurent SCHWARTZ Lebesgue Lemma linear continuous form Lipschitz boundary Lipschitz continuous Lº(N Lº(RN Lorentz spaces LP RN maps mathematical mathematician nonnegative normed space open set Poincaré's inequality Proof prove Radon measure result S(RN satisfies scalar Sergei SOBOLEV smoothing sequence Sobolev spaces Sobolev's embedding theorem solution space of functions subset subspace traces WS,P(RN ди მე