TY  - BOOK
AU  - Borsuk,Mikhail
AU  - Kondrat�ev,V.P.
TI  - Elliptic boundary value problems of second order in piecewise smooth domains
T2  - North-Holland mathematical library
SN  - 9780444521095
AV  - QA379 .B67 2006eb
U1  - 515/.3533 22
PY  - 2006///
CY  - Amsterdam, Boston
PB  - Elsevier
KW  - Boundary value problems
KW  - Differential equations, Elliptic
KW  - MATHEMATICS
KW  - Differential Equations
KW  - Partial
KW  - bisacsh
KW  - local
KW  - fast
KW  - Electronic books
N1  - 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
N2  - 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
UR  - http://www.sciencedirect.com/science/book/9780444521095
UR  - http://www.sciencedirect.com/science/publication?issn=09246509&volume=69
ER  -