Classical Potential Theory

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Gardiner Published DOI: Harmonic Functions. Laplace's equation. The mean value property. The Poisson integral for a ball. Harnack's inequalities. Families of harmonic functions: convergence properties. The Kelvin transform. Harmonic functions on half-spaces. Real-analyticity of harmonic functions.

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Harmonic Polynomials. Spaces of homogeneous polynomials. Another inner product on a space of polynomials. View via Publisher.

Classical Potential Theory, Book by David H. Armitage (Paperback) | duqehovy.tk

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  • Additional Material for the Book.
  • The Cauchy Transform, Potential Theory and Conformal Mapping.
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Classical Potential Theory by David H. Armitage , Stephen J. Gardiner Paperback October 4, Prices and offers may vary in store. From its origins in Newtonian physics, potential theory has developed into a major field of mathematical research. This book provides a comprehensive treatment of classical potential theory: it covers harmonic and subharmonic functions, maximum principles, polynomial expansions, Green functions, potentials and capacity, the Dirichlet problem and boundary integral representations. The first six chapters deal concretely with the basic theory, and include exercises.

The final three chapters are more advanced and treat topological ideas specifically created for potential theory, such as the fine topology, the Martin boundary and minimal thinness. The presentation is largely self-contained and is accessible to graduate students, the only prerequisites being a reasonable grounding in analysis and several variables calculus, and a first course in measure theory.

Classical potential theory

The book will prove an essential reference to all those with an interest in potential theory and its applications. Customer Reviews of Classical Potential Theory. Select Parent Grandparent Teacher Kid at heart. Age of the child I gave this to:. Hours of Play:.

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Your review has been submitted and will appear here shortly. Extra Content. Table of Contents 1. Harmonic Functions. Laplace's equation. The mean value property. The Poisson integral for a ball. Harnack's inequalities. Families of harmonic functions: convergence properties.

Potential theory

The Kelvin transform. Harmonic functions on half-spaces. Real-analyticity of harmonic functions. Harmonic Polynomials. Spaces of homogeneous polynomials. Another inner product on a space of polynomials.

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Axially symmetric harmonic polynomials. Polynomial expansions of harmonic functions. Laurent expansions of harmonic functions. Harmonic approximation. Harmonic polynomials and classical polynomials. Subharmonic Functions. Elementary properties.

Criteria for subharmonicity. Approximation of subharmonic functions by smooth ones. Convexity and subharmonicity. Mean values and subharmonicity. Harmonic majorants. Families of subharmonic functions: convergence properties. Green functions.

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The distributional Laplacian.

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