اصول حداکثری و ثوابت تیز برای راه‌حل‌های سیستم‌های بیضوی و پارابولیک (مجموعه بررسی‌ها و مونوگراف‌ها)

"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" --Back cover Cover 1 Title page 4 Contents 6 Introduction 10 Part I. Elliptic equations and systems 16 Prerequisites on operators acting into finite dimensional spaces 18 Maximum modulus principle for second order strongly elliptic systems 30 Sharp constants in the Miranda-Agmon inequalities for solutions of certain systems of mathematical physics 64 Sharp pointwise estimates for solutions of elliptic systems with boundary data from L^{p} 86 Sharp constant in the Miranda-Agmon type inequality for derivatives of solutions to higher order elliptic equation 102 Sharp pointwise estimates for directional derivatives and Khavinson’s type extremal problems for harmonic functions 114 The norm and the essential norm for double layer vector-valued potentials 160 Part II. Parabolic systems 210 Maximum modulus principle for parabolic systems 212 Maximum modulus principle for parabolic systems with zero boundary data 246 Maximum norm principle for parabolic systems without lower order terms 260 Maximum norm principle with respect to smooth norms for parabolic systems 286 Bibliography 306 List of symbols 316 Index 322 Back Cover 330 Prerequisites On Operators Acting Into Finite Dimensional Spaces -- Maximum Modulus Principle For Second Order Strongly Elliptic Systems -- Sharp Constants In The Miranda-agmon Inequalities For Solutions Of Certain Systems Of Mathematical Physics -- Sharp Pointwise Estimates For Solutions Of Elliptic Systems With Boundary Data From Lp -- Sharp Constant In The Miranda-agmon Type Inequality For Derivatives Of Solutions To Higher Order Elliptic Equations -- Sharp Pointwise Estimates For Directional Derivatives And Khavinson's Type Extremal Problems For Harmonic Functions -- The Norm And The Essential Norm For Double Layer Vector-valued Porentials -- Maximum Modulus Principle For Parabolic Systems -- Maximun Modulus Principle For Parabolic Systems Without Lower Order Terms -- Maximum Norm Principle With Respect To Smooth Norms For Parabolic Systems Gershon Kresin, Vladimir Maz'ya. Includes Bibliographical References And Index.