| Edition |
1st ed. |
| Description |
1 online resource (v, 531 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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text file |
| Series |
North-Holland mathematical library ; v. 69 |
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North-Holland mathematical library ; v. 69.
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| Summary |
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. |
| 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. |
| Bibliography |
Includes bibliographical references (pages 497-525) and indexes. |
| Note |
Print version record. |
| Subject |
Boundary value problems.
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Differential equations, Elliptic.
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Problèmes aux limites.
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Équations différentielles elliptiques.
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MATHEMATICS -- Differential Equations -- Partial.
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Boundary value problems
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Differential equations, Elliptic
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| Added Author |
Kondratev, V. P. (Vladimir Pavlovich)
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| Other Form: |
Print version: Borsuk, Mikhail. Elliptic boundary value problems of second order in piecewise smooth domains. 1st ed. Amsterdam ; Boston : Elsevier, 2006 0444521097 9780444521095 (DLC) 2005044878 (OCoLC)62408774 |
| ISBN |
9780444521095 |
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0444521097 |
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0080461735 (electronic bk.) |
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9780080461731 (electronic bk.) |
| Standard No. |
AU@ 000048130941 |
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CHNEW 001006655 |
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DEBBG BV036962358 |
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DEBBG BV039830226 |
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DEBBG BV042317350 |
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DEBSZ 276298144 |
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DEBSZ 482355948 |
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NZ1 12435167 |
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YDXCP 2495588 |
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AU@ 000075313955 |
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