The theory of Lebesgue and Sobolev spaces with variable
integrability is experiencing a steady expansion, and is the
subject of much vigorous research by functional analysts,
function-space analysts and specialists in nonlinear analysis.
These spaces have attracted attention not only because of their
intrinsic mathematical importance as natural, interesting examples
of non-rearrangement-invariant function spaces but also in view of
their applications, which include the mathematical modeling of
electrorheological fluids and image restoration.The main focus of
this book is to provide a solid functional-analytic background for
the study of differential operators on spaces with variable
integrability. It includes some novel stability phenomena which the
authors have recently discovered.At the present time, this is the
only book which focuses systematically on differential operators on
spaces with variable integrability. The authors present a concise,
natural introduction to the basic material and steadily move toward
differential operators on these spaces, leading the reader quickly
to current research topics.
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