Elliptic boundary value problems of second order in piecewise smooth domains
Author(s)
Bibliographic Information
Elliptic boundary value problems of second order in piecewise smooth domains
(North-Holland mathematical library, v. 69)
Elsevier, 2006
Available at 28 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
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  Switzerland
  France
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Note
Bibliography: p. 497-525
Includes indexes
Description and Table of Contents
Description
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.
Table of Contents
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.
by "Nielsen BookData"