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AuthorHoradam, A. F. editor
TitleQuasiconformal Mappings and Sobolev Spaces [electronic resource] / by V. M. Gol'dshtein, Yu. G. Reshetnyak
ImprintDordrecht : Springer Netherlands, 1990
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Descript XX, 372 p. online resource


1. Preliminary Information about Integration Theory -- ยง1. Notation and Terminology -- ยง2. Some Auxiliary Information about Sets and Functions in Rn -- ยง3. General Information about Measures and Integrals -- ยง4. Differentiation Theorems for Measures in Rn -- ยง5. Generalized Functions -- 2. Functions with Generalized Derivatives -- ยง1. Sobolev-Type Integral Representations -- ยง2. Other Integral Representations -- ยง3. Estimates for Potential-Type Integrals -- ยง4. Classes of Functions with Generalized Derivatives -- ยง5. Theorem on the Differentiability Almost Everywhere -- 3. Nonlinear Capacity -- ยง1. Capacity Induced by a Linear Positive Operator -- ยง2. The Classes W(T, p, V) -- ยง3. Sets Measurable with Respect to Capacity -- ยง4. Variational Capacity -- ยง5. Capacity in Sobolev Spaces -- ยง6. Estimates of [l, p]-Capacity for Some Pairs of Sets -- ยง7. Capacity in Besov-Nickolsky Spaces -- 4. Density of Extremal Functions in Sobolev Spaces with First Generalized Derivatives -- ยง1. Extremal Functions for (l, p)-Capacity -- ยง2. Theorem on the Approximation of Functions from Lpl by Extremal Functions -- ยง3. Removable Singularities for the Spaces Lpl (G) -- 5. Change of Variables -- ยง1. Multiplicity of Mapping, Degree of Mapping, and Their Analogies -- ยง2. The Change of Variable in the Integral for Mappings of Sobolev Spaces -- ยง3. Sufficient Conditions of Monotonicity and Continuity for the Approximation Functions of the Class Lnl -- ยง4. Invariance of the Spaces Lpl(G)(Lnl(G)) for Quasiisometric (Quasiconformal) Homeomorphisms -- 6. Extension of Differentiate Functions -- ยง1. Arc Diameter Condition -- ยง2. Necessary Extension Conditions for Seminormed Spaces -- ยง3. Necessary Extension Conditions for Sobolev Spaces -- ยง4. Necessary Extension Conditions for Besov and Nickolsky Spaces -- ยง5. Sufficient Extension Conditions -- Comments -- References

Mathematics Difference equations Functional equations Measure theory Functions of real variables Mathematics Measure and Integration Difference and Functional Equations Real Functions


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