
Introduction  Table of Contents  Index  Supplementary Material 
Mathematical Surveys and Monographs 2012; 317 pp; hardcover Volume: 183 ISBN10: 0821889818 ISBN13: 9780821889817 List Price: US$96 Member Price: US$76.80 Order Code: SURV/183 See also: Elliptic Equations in Polyhedral Domains  Vladimir Maz'ya and Jurgen Rossmann Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations  V A Kozlov, V G Maz'ya and J Rossmann  The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of MirandaAgmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrixvalued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations. Readership Graduate students and research mathematicians interested in partial differential equations. 


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