Isolated Singularities in Partial Differential Inequalities

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Differential Equations
Cover of the book Isolated Singularities in Partial Differential Inequalities by Marius Ghergu, Steven D. Taliaferro, Cambridge University Press
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Author: Marius Ghergu, Steven D. Taliaferro ISBN: 9781316494585
Publisher: Cambridge University Press Publication: January 25, 2016
Imprint: Cambridge University Press Language: English
Author: Marius Ghergu, Steven D. Taliaferro
ISBN: 9781316494585
Publisher: Cambridge University Press
Publication: January 25, 2016
Imprint: Cambridge University Press
Language: English

In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.

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In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.

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