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Catalogue Information
Field name	Details
Dewey Class	515.42
Title	Quasiconformal Mappings and Sobolev Spaces ([EBook]) / by V. M. Gol’dshtein, Yu. G. Reshetnyak.
Author	Goldshtein, Vladimir Mikhailovich
Added Personal Name	Reshetnyak, Yurii Grigor'evich
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1990.
Physical Details	XX, 372 pages : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 54
ISBN	9789400919228
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-009-1922-8
Links to Related Works	Subject References: Difference and Functional Equations . Difference equations . Functional equations . Functions of real variables . Mathematics . Measure and Integration . Measure theory . Quasiconformal mappings . Real Functions . Authors: author . Goldshtein, Vladimir Mikhailovich . Reshetnyak, Yurii Grigor'evich . See Also: Gol'dštein, V. M. . Golʹdshtein, Vladimir Mikhaĭlovich . Golʹdshteĭn, V. M. (Vladimir Mikhaĭlovich) . Golʹdštein, Vladimir Michajlovič . Rešetnjak, Jurij G. . Rešetnjak, Jurij Grigorʹevič . Решетняк, Юрий Григорьевич . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 515.42 .

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Quasiconformal Mappings and Sobolev Spaces

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