Parabolic Systems With Polynomial Growth And Regularity
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Parabolic Systems With Polynomial Growth And Regularity
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Author : Frank Duzaar
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Parabolic Systems With Polynomial Growth And Regularity written by Frank Duzaar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $ u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $ a(x,t,u,Du) \leq L(1+ Du ^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.
Parabolic Systems With Polynomial Growth And Regularity
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Author : Frank Duzaar
language : en
Publisher:
Release Date : 2011
Parabolic Systems With Polynomial Growth And Regularity written by Frank Duzaar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with MATHEMATICS categories.
The Regularity Of General Parabolic Systems With Degenerate Diffusion
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Author : Verena Bögelein
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-01-28
The Regularity Of General Parabolic Systems With Degenerate Diffusion written by Verena Bögelein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-28 with Mathematics categories.
The aim of the paper is twofold. On one hand the authors want to present a new technique called $p$-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classical tool to prove linearization and regularity results for vectorial problems. Here the authors develop a very far reaching version of this general principle devised to linearize general degenerate parabolic systems. The use of this result in turn allows the authors to achieve the subsequent and main aim of the paper, that is, the implementation of a partial regularity theory for parabolic systems with degenerate diffusion of the type $\partial_t u - \mathrm{div} a(Du)=0$, without necessarily assuming a quasi-diagonal structure, i.e. a structure prescribing that the gradient non-linearities depend only on the the explicit scalar quantity.
Linear And Quasilinear Parabolic Systems Sobolev Space Theory
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Author : David Hoff
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-11-18
Linear And Quasilinear Parabolic Systems Sobolev Space Theory written by David Hoff and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-18 with Education categories.
This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
Regularity Theory For Generalized Navier Stokes Equations
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Author : Cholmin Sin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-03-17
Regularity Theory For Generalized Navier Stokes Equations written by Cholmin Sin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-17 with Mathematics categories.
This book delves into the recent findings and research methods in the existence and regularity theory for Non-Newtonian Fluids with Variable Power-Law. The aim of this book is not only to introduce recent results and research methods in the existence and regularity theory, such as higher integrability, higher differentiability, and Holder continuity for flows of non-Newtonian fluids with variable power-laws, but also to summarize much of the existing literature concerning these topics. While this book mainly focuses on steady-state flows of non-Newtonian fluids, the methods and ideas presented in this book can be applied to unsteady flows (as discussed in Chapter 7) and other related problems such as complex non-Newtonian fluids, plasticity, elasticity, p(x)-Laplacian type systems, and so on. The book is intended for researchers and graduate students in the field of mathematical fluid mechanics and partial differential equations with variable exponents. It is expected to contribute to the advancement of mathematics and its applications.
The Goodwillie Tower And The Ehp Sequence
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Author : Mark Behrens
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
The Goodwillie Tower And The Ehp Sequence written by Mark Behrens and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The author studies the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime $2$. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. He relates the Goodwillie filtration to the $P$ map, and the Goodwillie differentials to the $H$ map. Furthermore, he studies an iterated Atiyah-Hirzebruch spectral sequence approach to the homotopy of the layers of the Goodwillie tower of the identity on spheres. He shows that differentials in these spectral sequences give rise to differentials in the EHP spectral sequence. He uses his theory to recompute the $2$-primary unstable stems through the Toda range (up to the $19$-stem). He also studies the homological behavior of the interaction between the EHP sequence and the Goodwillie tower of the identity. This homological analysis involves the introduction of Dyer-Lashof-like operations associated to M. Ching's operad structure on the derivatives of the identity. These operations act on the mod $2$ stable homology of the Goodwillie layers of any functor from spaces to spaces.
Second Order Analysis On Mathscr P 2 M W 2
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Author : Nicola Gigli
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-02-22
Second Order Analysis On Mathscr P 2 M W 2 written by Nicola Gigli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-22 with Mathematics categories.
The author develops a rigorous second order analysis on the space of probability measures on a Riemannian manifold endowed with the quadratic optimal transport distance $W_2$. The discussion includes: definition of covariant derivative, discussion of the problem of existence of parallel transport, calculus of the Riemannian curvature tensor, differentiability of the exponential map and existence of Jacobi fields. This approach does not require any smoothness assumption on the measures considered.
Nonlinear Partial Differential Equations And Related Topics
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Author : Arina A. Arkhipova
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Nonlinear Partial Differential Equations And Related Topics written by Arina A. Arkhipova and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"St. Petersburg PDE seminar, special session dedicated to N.N. Uraltseva's [75th] anniversary, June 2009"--P. [vi].
Parabolic Systems With Polynomial Growth And Regularity
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Author : Frank Duzaar
language : en
Publisher: American Mathematical Soc.
Release Date :
Parabolic Systems With Polynomial Growth And Regularity written by Frank Duzaar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"November 2011, volume 214, number 1005 (first of 5 numbers )."
Jumping Numbers Of A Simple Complete Ideal In A Two Dimensional Regular Local Ring
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Author : Tarmo Järvilehto
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Jumping Numbers Of A Simple Complete Ideal In A Two Dimensional Regular Local Ring written by Tarmo Järvilehto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The multiplier ideals of an ideal in a regular local ring form a family of ideals parameterized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript the author gives an explicit formula for the jumping numbers of a simple complete ideal in a two-dimensional regular local ring. In particular, he obtains a formula for the jumping numbers of an analytically irreducible plane curve. He then shows that the jumping numbers determine the equisingularity class of the curve.