The monograph jointly published by Marius Ghergu (UCD School of Mathematics and Statistics) and Steven D. Taliaferro (Texas A&M University) presents some methods for dealing with isolated singularities in elliptic and parabolic partial differential inequalities.
The main feature is that the authors investigate inequalities rather than equations, the reason being that the simplest way to study an equation is often to study the corresponding inequality; for example, using sub and superharmopnic functions to study harmonic functions. Another unusual feature is that the book 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 appeals 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. Isolated Singularities in Partial differential Inequalities is published by Cambridge University Press.