Quasiconformal Mappings and Sobolev Spaces

Inhaltsverzeichnis

• 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.