Elliptic boundary value problems of second order in piecewise smooth domains [electronic resource]
- 作者： Borsuk, Mikhail.
- 其他作者：
- 出版： Amsterdam ;Boston : Elsevier
- 版本：1st ed.
- 叢書名： North-Holland mathematical library,v. 69
- 主題： Boundary value problems , Differential equations, Elliptic , Electronic books.
- ISBN： 9780444521095 、 0444521097
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FIND@SFXID:
CGU
- 資料類型: 電子書
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內容註:
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.
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摘要註:
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.
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讀者標籤：
- 系統號： 005051655 | 機讀編目格式
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