Estimates for solutions to nonlinear boundary-value problems in conic domains
Gadjiev, Tahir S.
Aliev, Sardar Y.
Texas State University-San Marcos, Department of Mathematics
We obtain sharp estimates on the solution and its derivative near the conic points. In particular, we show that the solution satisfies |u(x)| ≤ C|x|λ where lambda is an eigenvalue of the Sturm-Liouville problem. Also we prove that the solution has square summable weighted second generalized derivatives.
Nonlinear equation, Behavior of solutions, Nonsmooth domain
Gadjiev, T. S., & Aliev, S. Y. (2005). Estimates for solutions to nonlinear boundary-value problems in conic domains. <i>Electronic Journal of Differential Equations, 2005</i>(16), pp. 1-8.