Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations [Reprint ed.] 3110151138, 9783110151138
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear an
222 27 3MB
English Pages 560 [556] Year 2011
Table of contents :
1 Introduction
2 Function spaces of Besov-Triebel-Lizorkin type
2.1 Definitions and fundamental properties
2.2 Embeddings
2.3 Some equivalent characterizations of Fsp,qand Bsp,q
2.4 Spaces on domains
2.5 Interpolation
2.6 Homogeneous spaces and a further supplement
3 Regular elliptic boundary value problems
3.1 Definitions and preliminaries
3.2 Estimates of integral operators
3.3 Estimates of the Poisson integral
3.4 A priori estimates
3.5 Regular elliptic boundary value problems
4 Pointwise multiplication
4.1 Introduction
4.2 The definition of the product
4.3 Necessary conditions for pointwise multiplication
4.4 Products of a function and a distribution
4.5 Products of functions and a distribution. The general case
4.6 The case of constant p
4.7 The extremal case p1 = p and p2 = .
4.8 Generalized Holder inequalities
4.9 The spaces Asp,q,unif and relations to M(Asp,q)
5 Nemytskij operators in spaces of Besov-Triebel-Lizorkin type
5.1 Introduction
5.2 Nemytskij operators in Lebesgue and Sobolev spaces
5.3 The Composition operator corresponding to a C.-function G in and Bsp
1 Introduction
2 Function spaces of Besov-Triebel-Lizorkin type
2.1 Definitions and fundamental properties
2.2 Embeddings
2.3 Some equivalent characterizations of Fsp,qand Bsp,q
2.4 Spaces on domains
2.5 Interpolation
2.6 Homogeneous spaces and a further supplement
3 Regular elliptic boundary value problems
3.1 Definitions and preliminaries
3.2 Estimates of integral operators
3.3 Estimates of the Poisson integral
3.4 A priori estimates
3.5 Regular elliptic boundary value problems
4 Pointwise multiplication
4.1 Introduction
4.2 The definition of the product
4.3 Necessary conditions for pointwise multiplication
4.4 Products of a function and a distribution
4.5 Products of functions and a distribution. The general case
4.6 The case of constant p
4.7 The extremal case p1 = p and p2 = .
4.8 Generalized Holder inequalities
4.9 The spaces Asp,q,unif and relations to M(Asp,q)
5 Nemytskij operators in spaces of Besov-Triebel-Lizorkin type
5.1 Introduction
5.2 Nemytskij operators in Lebesgue and Sobolev spaces
5.3 The Composition operator corresponding to a C.-function G in and Bsp
![Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations [Reprint ed.]
3110151138, 9783110151138](https://ebin.pub/img/200x200/sobolev-spaces-of-fractional-order-nemytskij-operators-and-nonlinear-partial-differential-equations-reprintnbsped-3110151138-9783110151138.jpg)
- Author / Uploaded
- Thomas Runst
![Fuzzy Fractional Differential Operators and Equations: Fuzzy Fractional Differential Equations [1st ed.]
9783030512712, 9783030512729](https://ebin.pub/img/200x200/fuzzy-fractional-differential-operators-and-equations-fuzzy-fractional-differential-equations-1st-ed-9783030512712-9783030512729.jpg)
![Fractional Partial Differential Equations [1 ed.]
9789811290404, 9789811290411, 9789811290428](https://ebin.pub/img/200x200/fractional-partial-differential-equations-1nbsped-9789811290404-9789811290411-9789811290428.jpg)
![Nonlinear Partial Differential Equations in Engineering [2]
0120567555, 9780120567553](https://ebin.pub/img/200x200/nonlinear-partial-differential-equations-in-engineering-2-0120567555-9780120567553.jpg)
![Second order partial differential equations in Hilbert spaces [1st ed.]
0521777291, 9780521777292, 9780511040863](https://ebin.pub/img/200x200/second-order-partial-differential-equations-in-hilbert-spaces-1stnbsped-0521777291-9780521777292-9780511040863.jpg)
![Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations [1 ed.]
9780367206291, 9780429262593](https://ebin.pub/img/200x200/semigroups-of-bounded-operators-and-second-order-elliptic-and-parabolic-partial-differential-equations-1nbsped-9780367206291-9780429262593.jpg)