2012/08/15 by Gershon Kresin, Vladimir Maz’ya · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Applied mathematics #Computer science #Constant (computer programming) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Mathematical analysis #Mathematics
paper · doi:10.1090/surv/183
openalex publication_date 2012/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 Miranda-Agmon 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 matrix-valued 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.