عنوان

Quasiconformal Mappings and Sobolev Spaces

(Number (ISBN

9400919220

(Number (ISBN

9789400919228

Number

b592739

Title Proper

Quasiconformal Mappings and Sobolev Spaces

General Material Designation

[Book]

First Statement of Responsibility

by V. M. Gol'dshtein, Yu. G. Reshetnyak.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands

Date of Publication, Distribution, etc.

1990

Specific Material Designation and Extent of Item

(XX, 372 p.).

Series Title

Mathematics and its Applications, Soviet Series, 54.

Text of Note

Bibliographic Level Mode of Issuance: Monograph.

Text of 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.

Functional equations.

Mathematics.

Measure and Integration.

Class number

Book number

by V. M. Gol'dshtein, Yu. G. Reshetnyak.

V M Gol'dshtein

Yu G Reshetnyak

Electronic name

[Book]

Y