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＜E-Book＞
Quasiconformal Mappings and Sobolev Spaces / by V.M. Gol'dshtein, Yu.G. Reshetnyak
(Mathematics and its Applications, Soviet Series ; 54)

Edition	1st ed. 1990.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	1990
Language	English
Size	XX, 372 p : online resource
Authors	*Gol'dshtein, V.M author Reshetnyak, Yu.G author SpringerLink (Online service)
Subjects	LCSH:Measure theory LCSH:Difference equations LCSH:Functional equations LCSH:Functions of real variables FREE:Measure and Integration FREE:Difference and Functional Equations FREE:Real Functions
Notes	1. Preliminary Information about Integration Theory -- §1. Notation and Terminology -- §2. Some Auxiliary Information about Sets and Functions in Rn -- §3. General Information about Measures and Integrals -- §4. Differentiation Theorems for Measures in Rn -- §5. Generalized Functions -- 2. Functions with Generalized Derivatives -- §1. Sobolev-Type Integral Representations -- §2. Other Integral Representations -- §3. Estimates for Potential-Type Integrals -- §4. Classes of Functions with Generalized Derivatives -- §5. Theorem on the Differentiability Almost Everywhere -- 3. Nonlinear Capacity -- §1. Capacity Induced by a Linear Positive Operator -- §2. The Classes W(T, p, V) -- §3. Sets Measurable with Respect to Capacity -- §4. Variational Capacity -- §5. Capacity in Sobolev Spaces -- §6. Estimates of [l, p]-Capacity for Some Pairs of Sets -- §7. Capacity in Besov-Nickolsky Spaces -- 4. Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives -- §1. Extremal Functions for (l, p)-Capacity -- §2. Theorem on the Approximation of Functions from Lpl by Extremal Functions -- §3. Removable Singularities for the Spaces Lpl (G) -- 5. Change of Variables -- §1. Multiplicity of Mapping, Degree of Mapping, and Their Analogies -- §2. The Change of Variable in the Integral for Mappings of Sobolev Spaces -- §3. Sufficient Conditions of Monotonicity and Continuity for the Approximation Functions of the Class Lnl -- §4. Invariance of the Spaces Lpl(G)(Lnl(G)) for Quasiisometric (Quasiconformal) Homeomorphisms -- 6. Extension of Differentiate Functions -- §1. Arc Diameter Condition -- §2. Necessary Extension Conditions for Seminormed Spaces -- §3. Necessary Extension Conditions for Sobolev Spaces -- §4. Necessary Extension Conditions for Besov and Nickolsky Spaces.-§5. Sufficient Extension Conditions -- Comments -- References HTTP:URL=https://doi.org/10.1007/978-94-009-1922-8

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