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

Quasiconformal Mappings and Sobolev Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

Zur Zeit liegt uns keine Inhaltsangabe vor.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 372
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9789400919228
• Artikelnr.: 44180494

Inhaltsangabe

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.