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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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