Identifiant pérenne de la notice : 21314722X
Notice de type
Notice de regroupement
Note publique d'information : Linear and non-linear elliptic boundary problems are a fundamental subject in analysis
and the spaces of weakly differentiable functions (also called Sobolev spaces) are
an essential tool for analysing the regularity of its solutions. The complete theory
of Sobolev spaces is covered whilst also explaining how abstract convex analysis can
be combined with this theory to produce existence results for the solutions of non-linear
elliptic boundary problems. Other kinds of functional spaces are also included, useful
for treating variational problems such as the minimal surface problem. Almost every
result comes with a complete and detailed proof. In some cases, more than one proof
is provided in order to highlight different aspects of the result. A range of exercises
of varying levels of difficulty concludes each chapter with hints to solutions for
many of them. It is hoped that this book will provide a tool for graduate and postgraduate
students interested in partial differential equations, as well as a useful reference
for researchers active in the field. Prerequisites include a knowledge of classical
analysis, differential calculus, Banach and Hilbert spaces, integration and the related
standard functional spaces, as well as the Fourier transformation on Schwartz spaces
paprika.idref.fr
data.idref.fr
Documentation
