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Boundary Behavior of Solutions to El...

Maz'ya, Vladimir G.,

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Boundary Behavior of Solutions to Elliptic Equations in General Domains

Record Type:	Electronic resources : Monograph/item
Title/Author:	Boundary Behavior of Solutions to Elliptic Equations in General Domains/ Vladimir G. Maz'ya
Author:	Maz'ya, Vladimir G.,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2018,
Description:	1 online resource (441 pages)
Subject:	Differential equations -
Online resource:	https://doi.org/10.4171/190
Online resource:	https://www.ems-ph.org/img/books/mazya_mini.jpg
ISBN:	9783037196908

Boundary Behavior of Solutions to Elliptic Equations in General Domains
Maz'ya, Vladimir G.,

Boundary Behavior of Solutions to Elliptic Equations in General Domains[electronic resource] /Vladimir G. Maz'ya - Zuerich, Switzerland :European Mathematical Society Publishing House,2018 - 1 online resource (441 pages) - EMS Tracts in Mathematics (ETM)30.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

The present book is a detailed exposition of the author and his collaborators' work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as "piecewise smoothness" or being a "Lipschitz graph". The description of the boundary behavior of such solutions is one of the most difficult problems in the theory of partial differential equations. After the famous Wiener test, the main contributions to this area were made by the author. In particular, necessary and sufficient conditions for the validity of imbedding theorems are given, which provide criteria for the unique solvability of boundary value problems of second and higher order elliptic equations. Another striking result is a test for the regularity of a boundary point for polyharmonic equations. The book will be interesting and useful for a wide audience. It is intended for specialists and graduate students working in the theory of partial differential equations.

ISBN: 9783037196908

Standard No.: 10.4171/190doiSubjects--Topical Terms:

704075
Differential equations

Boundary Behavior of Solutions to Elliptic Equations in General Domains
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520 $a The present book is a detailed exposition of the author and his collaborators' work on boundedness, continuity, and differentiability properties of solutions to elliptic equations in general domains, that is, in domains that are not a priori restricted by assumptions such as "piecewise smoothness" or being a "Lipschitz graph". The description of the boundary behavior of such solutions is one of the most difficult problems in the theory of partial differential equations. After the famous Wiener test, the main contributions to this area were made by the author. In particular, necessary and sufficient conditions for the validity of imbedding theorems are given, which provide criteria for the unique solvability of boundary value problems of second and higher order elliptic equations. Another striking result is a test for the regularity of a boundary point for polyharmonic equations. The book will be interesting and useful for a wide audience. It is intended for specialists and graduate students working in the theory of partial differential equations.
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