Elliptic equations in polyhedral domains / Vladimir Maz'ya, Jürgen Rossmann.

Format:

Book

Author/Creator:

Mazʹi︠a︡, V. G., author.

Rossmann, J. (Jürgen), 1954- author.

Series:

Mathematical surveys and monographs ; no. 162.

Mathematical surveys and monographs ; volume 162

Language:

English

Subjects (All):

Differential equations, Elliptic.

Polyhedra--Models.

Polyhedra.

Boundary value problems.

Physical Description:

1 online resource (618 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2010]

Language Note:

English

Summary:

This is the first monograph which systematically treats elliptic boundary value problems in domains of polyhedral type. The authors mainly describe their own recent results focusing on the Dirichlet problem for linear strongly elliptic systems of arbitrary order, Neumann and mixed boundary value problems for second order systems, and on boundary value problems for the stationary Stokes and Navier-Stokes systems. A feature of the book is the systematic use of Green's matrices. Using estimates for the elements of these matrices, the authors obtain solvability and regularity theorems for the solutions in weighted and non-weighted Sobolev and Holder spaces. Some classical problems of mathematical physics (Laplace and biharmonic equations, Lame system) are considered as examples. Furthermore, the book contains maximum modulus estimates for the solutions and their derivatives. The exposition is self-contained, and an introductory chapter provides background material on the theory of elliptic boundary value problems in domains with smooth boundaries and in domains with conical points. The book is destined for graduate students and researchers working in elliptic partial differential equations and applications.

Contents:

Pt. 1. The Dirichlet problem for strongly elliptic systems in polyhedral domains

2. Neumann and mixed boundary value problems for second order systems in polyhedral domains

Pt. 3. Mixed boundary value problems for stationary stokes and Navier-Stokes systems in polyhedral domains.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1389-2