Sobolev SpacesElsevier, 26 de jun. de 2003 - 320 páginas Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences. This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.
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Conteúdo
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CHAPTER 3 THE SOBOLEV SPACES WmP Ω | 59 |
CHAPTER 4 THE SOBOLEV IMBEDDING THEOREM | 79 |
CHAPTER 5 INTERPOLATION EXTENSION AND APPROXIMATION THEOREMS | 135 |
CHAPTER 6 COMPACT IMBEDDINGS OF SOBOLEV SPACES | 167 |
CHAPTER 7 FRACTIONAL ORDER SPACES | 205 |
CHAPTER 8 ORLICZ SPACES AND ORLICZSOBOLEV SPACES | 261 |
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Termos e frases comuns
Banach space bdry Q belongs Besov spaces bounded C# Q Cauchy sequence cone condition continuous function converges COROLLARY denote dense domain Q domain S2 EA(Q edge length equivalent exists a constant extension operator finite volume Fourier transform function f Hence Hölder's inequality holds infinity integral interpolation intersection LA(Q Lebesgue LEMMA Let Let Q Let u e Lipschitz condition LP norms LP Q LP S2 LP spaces LP(R mapping measurable function N-function nonnegative normed space obtain open set Orlicz spaces Orlicz-Sobolev spaces Paragraph precompact proof of Theorem properties prove Q satisfies S2 satisfies satisfies the strong satisfying the cone segment condition simple functions Sobolev Imbedding Theorem Sobolev spaces strong local Lipschitz subset subspace suppose THEOREM Let topology u e LP(Q u e W"P(Q unbounded domains uniformly convex vector space vol(Q x e S2 zero