Inverse Logarithmic Potential Problem.

Intro -- Introduction -- Chapter 1. Formulation of Inverse Logarithmic Potential Problem. Fundamental Equation -- 1.1 Formulation of inverse problem -- 1.2 Nonlinear boundary value problem for mapping function -- 1.3 The analytic continuation of the potential across a boundary -- 1.4 The boundary analyticity of domain is a solution to an inverse problem -- 1.5 The structure of inverse problem solution. final solvability. Examples -- Chapter 2. Local Solvability of an Inverse Problem -- 2.1 Univalent function variation -- 2.2 Local theorem of existence -- 2.3 Linearization of the boundary value problem -- 2.4 The auxiliary problem -- 2.5 The Newton-Kantorovitch method -- 2.6 The explicit solution of the linear problem -- 2.7 The local uniqueness theorem -- 2.8 The density variation. The equivalent solution set of the inverse problems. Remarks -- 2.9 The complex-valued density case -- 2.10 Existence theorems for the inverse problem for small constant densities -- 2.11 Proof of theorems -- Chapter 3. The Estimate of Bounded Univalent Function Coefficients and Univalent Polynomials -- 3.1 Classical estimates. Classes of bounded functions and with bounded image area -- 3.2 The estimate of univalent polynomials coefficients -- 3.3 The Diedonne-Horowitz inequalities for univalent polynomials -- 3.4 Numerical estimates of univalent polynomials coefficients -- Chapter 4. Mass Potential Estimates. Necessary Conditions for Solvability. A Priori Estimates for Inverse Problem Solution -- 4.1 Exact estimates for a mass potential gradient in the three-dimensional case. Extremal domain -- 4.2 Exact estimates of logarithmic mass potential -- 4.3 A priori estimates for inverse potential problem solution -- 4.4 On zeros of a potential mass gradient -- 4.5 Estimates of mass potential derivatives in a fixed angle.

4.6 The estimates of the mass potential derivatives in the disk -- 4.7 The estimate of the mass potential based on the Calderon-Zygmund results for the singular integral -- 4.8 The necessary solvability conditions, a priori estimates - using the univalent function theory -- Chapter 5. The Continuation by the Parameter of an Inverse Problem Solution -- 5.1 The dependence of an inverse problem solution on the parameter - a constant density -- 5.2 The theorem on the continuation of a solution by the parameter -- 5.3 Inverse potential problems and univalent functions -- Chapter 6. On the Analyticity and Smoothness of an Inverse Problem Solution -- 6.1 Theorem on the smoothness of inverse problem solutions -- 6.2 Applications of the theorem on smoothness, in connection with free boundary smoothness -- 6.3 Analytical continuation of the potential through the angle points -- Chapter 7. Inverse Linear Problem. Determination of a Density of the Given Domain by its Exterior Potential -- 7.1 Existence theorems. The particular solutions of the inhomogeneous problem construction -- 7.2 Solution of the homogeneous problem. Density of the vanishing external potential -- 7.3 Special classes of domains -- 7.4 Determination of a body's density by the given potential of an elliptic equation -- 7.5 Linear inverse problem in the classes Lp -- Chapter 8. Conjugation of Harmonic and Analytic Functions: Direct and Inverse Problems -- 8.1 Problems of the linear conjugation for harmonic and analytic functions -- 8.2 The particular cases, modifications, applications and generalization of the base conjugation problem -- 8.3 Formulation of inverse problems -- 8.4 Applied inverse problems -- 8.5 Interior inverse problems -- Chapter 9. Applications in Gravity Prospecting and in Magnetic Prospecting.

9.1 Setting of problems. The algorithm for numerical construction of the equivalent solutions set by the analytically given field -- 9.2 On one approximation method (analytic continuation) for gravitational fields -- 9.3 Examples of the numerical constructing of the equivalent solutions family -- 9.4 Approximation of the anomaly field and determining the object by the random search method -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.