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" Quasiconformal Mappings and Sobolev Spaces "
by V. M. Gol’dshtein, Yu. G. Reshetnyak.
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BL
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| Record Number
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772745
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b592739
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| Main Entry
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by V. M. Gol’dshtein, Yu. G. Reshetnyak.
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| Title & Author
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Quasiconformal Mappings and Sobolev Spaces\ by V. M. Gol’dshtein, Yu. G. Reshetnyak.
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| Publication Statement
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Dordrecht : Springer Netherlands, 1990
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| Series Statement
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Mathematics and its Applications, Soviet Series, 54.
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| Page. NO
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(XX, 372 p.).
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| ISBN
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9400919220
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: 9789400919228
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| Notes
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Bibliographic Level Mode of Issuance: Monograph.
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| Contents
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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.
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| Subject
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Functional equations.
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Mathematics.
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Measure and Integration.
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| LC Classification
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QA360.B986 1990
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| Added Entry
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V M Gol’dshtein
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Yu G Reshetnyak
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