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Regularity Problem for Quasilinear Elliptic and Parabolic Systems

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 725/5 ( reviews)

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Book Synopsis Regularity Problem for Quasilinear Elliptic and Parabolic Systems by : Alexander Koshelev

Download or read book Regularity Problem for Quasilinear Elliptic and Parabolic Systems written by Alexander Koshelev. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described. The results presented are based on two main ideas: the universal iterative method, and explicit, sometimes sharp, coercivity estimates in weighted spaces. Readers are assumed to have a standard background in analysis and PDEs.

Linear and Quasilinear Parabolic Systems: Sobolev Space Theory

2020-11-18 Education
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Release : 2020-11-18
Genre : Education
Kind : eBook
Book Rating : 617/5 ( reviews)

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Book Synopsis Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by : David Hoff

Download or read book Linear and Quasilinear Parabolic Systems: Sobolev Space Theory written by David Hoff. This book was released on 2020-11-18. Available in PDF, EPUB and Kindle. Book excerpt: 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 Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions

1990 Mathematics
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Release : 1990
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions by : Friedmar Schulz

Download or read book Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions written by Friedmar Schulz. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.

Elliptic Regularity Theory

2016-04-08 Mathematics
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Release : 2016-04-08
Genre : Mathematics
Kind : eBook
Book Rating : 856/5 ( reviews)

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Book Synopsis Elliptic Regularity Theory by : Lisa Beck

Download or read book Elliptic Regularity Theory written by Lisa Beck. This book was released on 2016-04-08. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.

Strongly Coupled Parabolic and Elliptic Systems

2018-11-05 Mathematics
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Release : 2018-11-05
Genre : Mathematics
Kind : eBook
Book Rating : 766/5 ( reviews)

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Book Synopsis Strongly Coupled Parabolic and Elliptic Systems by : Dung Le

Download or read book Strongly Coupled Parabolic and Elliptic Systems written by Dung Le. This book was released on 2018-11-05. Available in PDF, EPUB and Kindle. Book excerpt: Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo–Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)–H1(μ)| Some algebraic inequalities Partial regularity

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