# Isolated singularities in partial differential inequalities / Marius Ghergu, University College Dublin, Steven D. Taliaferro, Texas A & M University.

##### By: Ghergu, Marius [author.].

##### Contributor(s): Taliaferro, Steven D [author.].

Material type: TextSeries: Encyclopedia of mathematics and its applications: no. 161.Publisher: Cambridge : Cambridge University Press, 2016Description: xii, 349 pages ; UKP 79.99 24 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781107138384; 1107138388.Subject(s): Inequalities (Mathematics) | Singularities (Mathematics) | Inequalities (Mathematics) | Singularities (Mathematics)DDC classification: 515.3/6 Online resources: Contributor biographical information | Publisher description | Table of contents onlyItem type | Current location | Call number | Status | Date due | Barcode | Item holds |
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Book | Chennai Mathematical Institute General Stacks | 515.36 GHE (Browse shelf) | Available | 10242 |

Includes bibliographical references and index.

Representation formulae for singular solutions of polyharmonic and parabolic inequalities -- Isolated singularities of nonlinear second-order elliptic inequalities -- More on isolated singularities for semilinear elliptic inequalities -- Elliptic inequalities for the Laplace operator with Hardy potential -- Singular solutions for second-order nondivergence type elliptic inequalities -- Isolated singularities of polyharmonic inequalities -- Isolated singularities of polyharmonic inequalities -- Nonlinear biharmonic inequalities -- Semilinear elliptic systems of differential inequalities -- Isolated singularities for nonlocal elliptic systems -- Isolated singularities for systems of parabolic inequalities -- Appendixes: A. Estimates for the heat kernel -- B. Heat potential estimates -- C. Nonlinear potential estimates.

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.-- Source other than the Library of Congress.