Function Spaces and Potential Theory

ADAMS, David R.; HEDBERG, Lars Inge

ISBN 10: 3540570608 / ISBN 13: 9783540570608

Edité par Springer, 1999

A propos de cet article

Grundlehren der mathematischen Wissenschaftern 314. A Series of Comprehensive Studies in Mathematics. xi, 366 p. 24 cm. Ex library with labels on spine and front, ink stamps on top edge and title.

N° de réf. du vendeur 147842

Détails bibliographiques

• Titre: Function Spaces and Potential Theory
• Éditeur: Springer
• Date de parution: 1999
• Langue: anglais
• ISBN à 10 chiffres: 3540570608
• ISBN à 13 chiffres: 9783540570608
• Reliure: Hardcover
• Édition: Corrected Second Printing.
• État de l'article: ex library-very good
• Catalogues du vendeur:
  • Science

A propos de ce titre

Synopsis

The subject of this book is the interplay between function space theory and potential theory. The theory has reached a state of maturity and elegance by now that makes it natural to present it in book form. The book is accessible to graduate students with a good background in real analysis. No previous knowlegde of potential theory is assumed.

Présentation de l'éditeur

The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square integrable. More recently, a generalized potential theory has been developed, which has an analogous relationship to the standard Banach function spaces, Sobolev spaces, Besov spaces etc., that appear naturally in the study of partial differential equations. A surprisingly large part of classical potential theory has been extended to this nonlinear setting. The extensions are sometimes surprising, usually they are nontrivial and have required new methods.