Linear Holomorphic Partial Differential Equations and Classical Potential Theory - Couverture rigide

Khavinson, Dmitry; Lundberg, Erik

Couverture rigide

ISBN 10 : 1470437805 ISBN 13 : 9781470437800

Editeur : American Mathematical Society, 2018

Synopsis

Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in ``physical'' mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1470437805
• ISBN 13: 9781470437800
• Reliure: Relié
• Nombre de pages: 212
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible