Inverse Logarithmic Potential Problem
eBook - PDF

Inverse Logarithmic Potential Problem

  1. 250 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Inverse Logarithmic Potential Problem

Book details
Table of contents
Citations

About This Book

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

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Yes, you can access Inverse Logarithmic Potential Problem by V. G. Cherednichenko in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2014
ISBN
9783110900125
Edition
1
Topic
Mathematics
Subtopic
Differential Equations
Index
Mathematics

Table of contents

  1. Introduction
  2. Chapter 1. Formulation of Inverse Logarithmic Potential Problem. Fundamental Equation
  3. §1.1 Formulation of inverse problem
  4. §1.2 Nonlinear boundary value problem for mapping function
  5. §1.3 The analytic continuation of the potential across a boundary
  6. §1.4 The boundary analyticity of domain is a solution to an inverse problem
  7. §1.5 The structure of inverse problem solution. final solvability. Examples
  8. Chapter 2. Local Solvability of an Inverse Problem
  9. §2.1 Univalent function variation
  10. §2.2 Local theorem of existence
  11. §2.3 Linearization of the boundary value problem
  12. §2.4 The auxiliary problem
  13. §2.5 The Newton-Kantorovitch method
  14. §2.6 The explicit solution of the linear problem
  15. §2.7 The local uniqueness theorem
  16. §2.8 The density variation. The equivalent solution set of the inverse problems. Remarks
  17. §2.9 The complex-valued density case
  18. §2.10 Existence theorems for the inverse problem for small constant densities
  19. §2.11 Proof of theorems
  20. Chapter 3. The Estimate of Bounded Univalent Function Coefficients and Univalent Polynomials
  21. §3.1 Classical estimates. Classes of bounded functions and with bounded image area
  22. §3.2 The estimate of univalent polynomials coefficients
  23. §3.3 The Diedonne-Horowitz inequalities for univalent polynomials
  24. §3.4 Numerical estimates of univalent polynomials coefficients
  25. Chapter 4. Mass Potential Estimates. Necessary Conditions for Solvability. A Priori Estimates for Inverse Problem Solution
  26. §4.1 Exact estimates for a mass potential gradient in the three-dimensional case. Extremal domain
  27. §4.2 Exact estimates of logarithmic mass potential
  28. §4.3 A priori estimates for inverse potential problem solution
  29. §4.4 On zeros of a potential mass gradient
  30. §4.5 Estimates of mass potential derivatives in a fixed angle
  31. §4.6 The estimates of the mass potential derivatives in the disk
  32. §4.7 The estimate of the mass potential based on the Calderon-Zygmund results for the singular integral
  33. §4.8 The necessary solvability conditions, a priori estimates — using the univalent function theory
  34. Chapter 5. The Continuation by the Parameter of an Inverse Problem Solution
  35. §5.1 The dependence of an inverse problem solution on the parameter - a constant density
  36. §5.2 The theorem on the continuation of a solution by the parameter
  37. §5.3 Inverse potential problems and univalent functions
  38. Chapter 6. On the Analyticity and Smoothness of an Inverse Problem Solution
  39. §6.1 Theorem on the smoothness of inverse problem solutions
  40. §6.2 Applications of the theorem on smoothness, in connection with free boundary smoothness
  41. §6.3 Analytical continuation of the potential through the angle points
  42. Chapter 7. Inverse Linear Problem. Determination of a Density of the Given Domain by its Exterior Potential
  43. §7.1 Existence theorems. The particular solutions of the inhomogeneous problem construction
  44. §7.2 Solution of the homogeneous problem. Density of the vanishing external potential
  45. §7.3 Special classes of domains
  46. §7.4 Determination of a body’s density by the given potential of an elliptic equation
  47. §7.5 Linear inverse problem in the classes Lp
  48. Chapter 8. Conjugation of Harmonic and Analytic Functions: Direct and Inverse Problems
  49. §8.1 Problems of the linear conjugation for harmonic and analytic functions
  50. §8.2 The particular cases, modifications, applications and generalization of the base conjugation problem
  51. §8.3 Formulation of inverse problems
  52. §8.4 Applied inverse problems
  53. §8.5 Interior inverse problems
  54. Chapter 9. Applications in Gravity Prospecting and in Magnetic Prospecting
  55. §9.1 Setting of problems. The algorithm for numerical construction of the equivalent solutions set by the analytically given field
  56. §9.2 On one approximation method (analytic continuation) for gravitational fields
  57. §9.3 Examples of the numerical constructing of the equivalent solutions family
  58. §9.4 Approximation of the anomaly field and determining the object by the random search method
  59. Bibliography