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Elliptic boundary value problems of second order in piecewise smooth domains

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elliptic boundary value problems of second order in piecewise smooth domains/ Mikhail Borsuk, Vladimir Kondratiev.
Author:	Borsuk, Mikhail.
other author:	Kondrat�ev, V. P.
Published:	Amsterdam ;Elsevier, : 2006.,
Description:	v, 531 p. :ill. ; : 24 cm.;
Series:	North-Holland mathematical library ;
Subject:	Boundary value problems. -
Online resource:	An electronic book accessible through the World Wide Web; click for information
ISBN:	9780444521095

Elliptic boundary value problems of second order in piecewise smooth domains
Borsuk, Mikhail.

Elliptic boundary value problems of second order in piecewise smooth domains[electronic resource] /Mikhail Borsuk, Vladimir Kondratiev. - 1st ed. - Amsterdam ;Elsevier,2006. - v, 531 p. :ill. ;24 cm. - North-Holland mathematical library ;v. 69.

Includes bibliographical references (p. 497-525) and indexes.

Introduction. -- 1. Preliminaries. -- 2. Integral inequalities. -- 3. The Laplace operator. -- 4. Strong solutions of the Dirichlet problem for linear equations. -- 5. The Dirichlet problem for elliptic linear. -- divergent equations in a nonsmooth domain. -- 6. The Dirichlet problem for semilinear equations in a conical domain. -- 7. Strong solutions of the Dirichlet problem for nondivergence quasilinear equations. -- 8. Weak solutions of the Dirichlet problem for elliptic divergence form quasilinear equations. -- 9. The behavior of weak solutions to the boundary value problems for elliptic quasilinear equations with triple degeneration in a neighborhood of a boundary edge. -- 10. Sharp estimates of solutions to the Robin. -- boundary value problem for elliptic non divergence second order equations in a neighborhood of the conical point. -- Bibliography. -- Notation Index. -- Index.

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy Friedrichs Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

Electronic reproduction.
Amsterdam :
Elsevier Science & Technology,
2007.

Mode of access: World Wide Web.

ISBN: 9780444521095

Source: 116412:116510Elsevier Science & Technologyhttp://www.sciencedirect.comSubjects--Topical Terms:

134906
Boundary value problems.
Index Terms--Genre/Form:

96803
Electronic books.

LC Class. No.: QA379 / .B67 2006eb

Dewey Class. No.: 515/.3533

Elliptic boundary value problems of second order in piecewise smooth domains
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020 $a 9780444521095
020 $a 0444521097
029 1 $a NZ1 $b 12435167
035 $a (OCoLC)162587091
035 $a ocn162587091
037 $a 116412:116510 $b Elsevier Science & Technology $n http://www.sciencedirect.com
040 $a OPELS $c OPELS $d OCLCG
049 $a TEFA
050 1 4 $a QA379 $b .B67 2006eb
082 0 4 $a 515/.3533 $2 22
100 1 $a Borsuk, Mikhail. $3 291456
245 1 0 $a Elliptic boundary value problems of second order in piecewise smooth domains $h [electronic resource] / $c Mikhail Borsuk, Vladimir Kondratiev.
250 $a 1st ed.
260 $a Amsterdam ; $a Boston : $c 2006. $b Elsevier,
300 $a v, 531 p. : $b ill. ; $c 24 cm.
440 0 $a North-Holland mathematical library ; $v v. 69
504 $a Includes bibliographical references (p. 497-525) and indexes.
505 0 $a Introduction. -- 1. Preliminaries. -- 2. Integral inequalities. -- 3. The Laplace operator. -- 4. Strong solutions of the Dirichlet problem for linear equations. -- 5. The Dirichlet problem for elliptic linear. -- divergent equations in a nonsmooth domain. -- 6. The Dirichlet problem for semilinear equations in a conical domain. -- 7. Strong solutions of the Dirichlet problem for nondivergence quasilinear equations. -- 8. Weak solutions of the Dirichlet problem for elliptic divergence form quasilinear equations. -- 9. The behavior of weak solutions to the boundary value problems for elliptic quasilinear equations with triple degeneration in a neighborhood of a boundary edge. -- 10. Sharp estimates of solutions to the Robin. -- boundary value problem for elliptic non divergence second order equations in a neighborhood of the conical point. -- Bibliography. -- Notation Index. -- Index.
520 $a The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. Key features: * New the Hardy Friedrichs Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration. * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. * The question about the influence of the coefficients smoothness on the regularity of solutions. * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems. * The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian. * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
533 $a Electronic reproduction. $b Amsterdam : $c Elsevier Science & Technology, $d 2007. $n Mode of access: World Wide Web. $n System requirements: Web browser. $n Title from title screen (viewed on Aug. 2, 2007). $n Access may be restricted to users at subscribing institutions.
650 0 $a Boundary value problems. $3 134906
650 0 $a Differential equations, Elliptic. $3 134927
655 7 $a Electronic books. $2 local. $3 96803
700 1 $a Kondrat�ev, V. P. $q (Vladimir Pavlovich) $3 291457
710 2 $a ScienceDirect (Online service) $3 254709
776 1 $c Original $z 0444521097 $z 9780444521095 $w (DLC) 2005044878 $w (OCoLC)62408774
856 4 0 $3 ScienceDirect $u http://www.sciencedirect.com/science/publication?issn=09246509&volume=69 $z An electronic book accessible through the World Wide Web; click for information
856 4 0 $3 Referex $u http://www.engineeringvillage.com/controller/servlet/OpenURL?genre=book&isbn=9780444521095 $z An electronic book accessible through the World Wide Web; click for information
856 4 2 $3 Publisher description $u http://www.loc.gov/catdir/enhancements/fy0624/2005044878-d.html
856 4 1 $3 Table of contents $u http://www.loc.gov/catdir/enhancements/fy0624/2005044878-t.html
994 $a C0 $b TEF

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