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Divided into two parts, this book targets graduate students and researchers who want to learn about variable Lebesgue spaces and partial differential equations. Part I provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces likethe classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally in the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. Part IIof...