Geodesic
Estimates for solutions to nonlinear boundary-value problems in conic domains
Electronic journal of differential equations, Tome 2005 (2005)
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.
Classification : 35J20, 35D10
Keywords: nonlinear equation, behavior of solutions, nonsmooth domain 
@article{EJDE_2005__2005__a153,
     author = {Gadjiev,  Tahir S. and Aliev,  Sardar Y.},
     title = {Estimates for solutions to nonlinear boundary-value problems in conic domains},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1129.35377},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a153/}
}
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Gadjiev,  Tahir S.; Aliev,  Sardar Y. Estimates for solutions to nonlinear boundary-value problems in conic domains. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a153/