Topics on Degenerate Elliptic Equations PDF Download

Author: Albo Carlos Cavalheiro
Publisher:
ISBN: 9783659818301
Category :
Languages : en
Pages : 252

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Author: Serge Levendorskii
Publisher:
ISBN:
Category :
Languages : en
Pages : 431

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Book Description

Author: Serge Levendorskii
Publisher: Springer Science & Business Media
ISBN: 9401712158
Category : Mathematics
Languages : en
Pages : 442

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Book Description
This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Grding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

Author: Albo Carlos Cavalheiro
Publisher: Cambridge Scholars Publishing
ISBN: 1527551679
Category : Mathematics
Languages : en
Pages : 333

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Book Description
In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.

Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 048682425X
Category : Mathematics
Languages : en
Pages : 417

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Book Description
A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.

Author: Michel Chipot
Publisher: Springer Science & Business Media
ISBN: 3764399813
Category : Mathematics
Languages : en
Pages : 289

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Book Description
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.

Author: Edward W. Stredulinsky
Publisher:
ISBN:
Category :
Languages : en
Pages : 142

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Book Description
Various weighted inequalities and weighted function spaces relevant to degenerate partial differential equations are studied. The results are applied to degenerate second order divergence form elliptic equations and systems to establish continuity of weak solutions. The methods used allow the consideration of very general classes of weights. In particular the weights are characterized for several Sobolev inequalities in terms of weighted capacities, a theorem is proven for weighted reverse Holder inequalities and a continuity estimate is established for certain weighted Sobolev spaces. (Author).

Author: Serge Levendorskii
Publisher: Springer Science & Business Media
ISBN: 9780792323051
Category : Mathematics
Languages : en
Pages : 458

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Book Description
This volume is the first to be devoted to the study of various properties of wide classes of degenerate elliptic operators of arbitrary order and pseudo-differential operators with multiple characteristics. Conditions for operators to be Fredholm in appropriate weighted Sobolev spaces are given, a priori estimates of solutions are derived, inequalities of the Gårding type are proved, and the principal term of the spectral asymptotics for self-adjoint operators is computed. A generalization of the classical Weyl formula is proposed. Some results are new, even for operators of the second order. In addition, an analogue of the Boutet de Monvel calculus is developed and the index is computed. For postgraduate and research mathematicians, physicists and engineers whose work involves the solution of partial differential equations.

Author: E. W. Stredulinsky
Publisher:
ISBN: 9783662189603
Category :
Languages : en
Pages : 156

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Book Description

Author: Nguyen Minh Tri
Publisher: LAP Lambert Academic Publishing
ISBN: 9783843371100
Category :
Languages : en
Pages : 276

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Book Description
Boundary value problems and smoothness of solutions to nonlinear elliptic equations and linear degenerate elliptic equations have been studied for more than a century. However, the study of nonlinear degenerate elliptic equations is not enough taken up. This book is based on research of the author on semilinear degenerate elliptic equations, i. e. nonlinear equations the principal parts of which are linear and degenerate elliptic. The first and second parts, after an introduction, cover the following topics: infinite differentiability, analyticity, Gevrey regularity of solutions. The third part is devoted to the study of the boundary value problems. Here the phenomena of critical exponents are discussed. This book will be a useful reference source for graduate students and researchers in differential equations, complex analysis, as well as in nonlinear analysis.