Elliptic boundary value problems of second order in piecewise smooth domains [EBook] / Mikhail Borsuk, Vladimir Kondratiev.
Elliptic boundary value problems of second order in piecewise smooth domains [EBook] / Mikhail Borsuk, Vladimir Kondratiev.
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in nonsmooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of...
Personal Name(s):  Borsuk, Mikhail. 

Kondratev, V. P.  
Edition: 
1st ed. 
Imprint: 
Amsterdam ; Boston :
Elsevier,
2006

Physical Description: 
1 online resource (v, 531 p.) : ill. 
Note: 
englisch 
ISBN: 
0080461735 9780444521095 9780080461731 0444521097 
Series Title: 
NorthHolland mathematical library ;
v. 69 
Subject (LOC):  
Full Text 
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in nonsmooth 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. 