Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 16, pp. 1-8.
Title: Estimates for solutions to nonlinear boundary-value
problems in conic domains
Authors: Tahir S. Gadjiev (Inst. Math. & Mechanics of NAS, Azerbaijan)
Sardar Y. Aliev (Baku State Univ., Azerbaijan)
Abstract:
We obtain sharp estimates on the solution and its
derivative near the conic points. In particular,
we show that the solution satisfies
$|u(x)|\leq C|x|^\lambda$
where lambda is an eigenvalue of the Sturm-Liouville problem.
Also we prove that the solution has square summable
weighted second generalized derivatives.
Submitted January 27, 2004. Published February 1, 2005.
Math Subject Classifications: 35J20, 35D10.
Key Words: Nonlinear equation; behavior of solutions; nonsmooth domain.