ELLIPTIC BOUNDARY VALUE PROBLEMS OF SECOND ORDER IN PIECEWISE SMOOTH DOMAINS, 69
To order this title, and for more information, click here
By Michail Borsuk, Dr. Sci. in Mathematics, University of Warmia and Mazury in Olsztyn, Poland Vladimir Kondratiev, Dr. Sci. in Mathematics, Moscow State University, Russia
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.
Audience
Researchers and graduate students working in the field of partial differential equations.
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.
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
Home | Elsevier Sites | Privacy Policy | Terms and Conditions | Feedback | Site Map | A Reed Elsevier Company