Electron. J. Diff. Eqns., Vol. 2005(2005), No. 16, pp. 1-8.

Estimates for solutions to nonlinear boundary-value problems in conic domains

Tahir S. Gadjiev, Sardar Y. Aliev

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.

An addendum has been attached on March 18, 2005.
It includes the reference
Borsuk, M. V.; Behavior of generalized solutions of the Dirichlet problem for second-order quasilinear elliptic equations of divergence type near a conical point. (Russian) Sibirsk. Mat. Zh. 31 (1990), no. 6, 25--38; translation in Siberian Math. J. 31 (1990), no. 6, 891--904 (1991)
and compares the results in this article with those in the new reference.

Submitted January 27, 2004. Published February 1, 2005.
Math Subject Classifications: 35J20, 35D10.
Key Words: Nonlinear equation; behavior of solutions; nonsmooth domain.

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Tahir S. Gadjiev
Institute of Mathematics & Mechanics of NAS Azerbaijan
Department of Nonlinear Analysis
9, F. Agayev str., AZ1141, Baku, Azerbaijan
email: tgadjiev@mail.az
Sardar Y. Aliev
Baku State University, Department of Mathematics
23 Z. Khalilov str., AZ1148, Baku, Azerbaijan
email: ibvag@yahoo.com

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