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This book provides a brief, self-contained introduction to Carleman
estimates for three typical second order partial differential
equations, namely elliptic, parabolic, and hyperbolic equations,
and their typical applications in control, unique continuation, and
inverse problems. There are three particularly important and novel
features of the book. First, only some basic calculus is needed in
order to obtain the main results presented, though some elementary
knowledge of functional analysis and partial differential equations
will be helpful in understanding them. Second, all Carleman
estimates in the book are derived from a fundamental identity for a
second order partial differential operator; the only difference is
the choice of weight functions. Third, only rather weak smoothness
and/or integrability conditions are needed for the coefficients
appearing in the equations. Carleman Estimates for Second Order
Partial Differential Operators and Applications will be of interest
to all researchers in the field.
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