maximum principles and sharp constants for solutions of elliptic and parabolic systems

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Maximum Principles And Sharp Constants For Solutions Of Elliptic And Parabolic Systems

Author : Gershon Kresin
ISBN : 9780821889817
Genre : Mathematics
File Size : 69. 28 MB
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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.

Functional Inequalities New Perspectives And New Applications

Author : Nassif Ghoussoub
ISBN : 9780821891520
Genre : Mathematics
File Size : 57. 8 MB
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"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.

The Octagonal Pets

Author : Richard Evan Schwartz
ISBN : 9781470415228
Genre : Mathematics
File Size : 39. 91 MB
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A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmüller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.

Mathematical Reviews

Author :
ISBN : UVA:X006180447
Genre : Mathematics
File Size : 30. 10 MB
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Regularity Problem For Quasilinear Elliptic And Parabolic Systems

Author : Aleksandr Ivanovich Koshelev
ISBN : 3540602518
Genre : Differential equations, Elliptic
File Size : 78. 87 MB
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Soviet Mathematics Doklady

Author :
ISBN : UCAL:B4492493
Genre : Mathematics
File Size : 81. 62 MB
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Pian Wei Fen Fang Cheng

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ISBN : UOM:39015058986434
Genre : Differential equations, Partial
File Size : 48. 59 MB
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