Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains PDF eBook
Author Vladimir Maz'ya
Publisher Birkhäuser
Pages 448
Release 2012-12-06
Genre Mathematics
ISBN 3034884346

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Book in PDF, Epub and Kindle

For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems.

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains PDF eBook
Author Vladimir Maz'ya
Publisher Birkhäuser
Pages 758
Release 2000-05-01
Genre Mathematics
ISBN 9783764329648

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Book in PDF, Epub and Kindle

For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the work is based on the authors' work and has no significant overlap with other books on the theory of elliptic boundary value problems.

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II PDF eBook
Author V. G. Mazʹi͡a︡
Publisher Springer Science & Business Media
Pages 362
Release 2000
Genre Boundary value problems
ISBN 9783764363987

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II Book in PDF, Epub and Kindle

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II PDF eBook
Author Vladimir Maz'ya
Publisher Birkhäuser
Pages 336
Release 2012-12-06
Genre Mathematics
ISBN 303488432X

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II Book in PDF, Epub and Kindle

For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II PDF eBook
Author Vladimir Maz'ya
Publisher Birkhäuser
Pages 323
Release 2011-11-22
Genre Mathematics
ISBN 9783034884334

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II Book in PDF, Epub and Kindle

For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains PDF eBook
Author Vladimir Maz'ya
Publisher Birkhäuser
Pages 0
Release 2000-05-01
Genre Mathematics
ISBN 9783764329648

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Book in PDF, Epub and Kindle

For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the work is based on the authors' work and has no significant overlap with other books on the theory of elliptic boundary value problems.

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
Title Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains PDF eBook
Author V. Maz'ya
Publisher
Pages
Release 2000
Genre
ISBN 9780817663988

Download Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Book in PDF, Epub and Kindle