The aim of this book is to introduce the reader to different topics of
the theory of elliptic partial differential equations by avoiding
technicalities and refinements. Apart from the basic theory of equations
in divergence form it includes subjects such as singular perturbation
problems, homogenization, computations, asymptotic behaviour of problems
in cylinders, elliptic systems, nonlinear problems, regularity theory,
Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev
spaces has been introduced, and work or integration on the boundary has
been carefully avoided to keep the reader's attention on the beauty and
variety of these issues.
The chapters are relatively independent of each other and can be read or
taught separately. Numerous results presented here are original and have
not been published elsewhere. The book will be of interest to graduate
students and faculty members specializing in partial differential
equations.