We deal with the Dirichlet problem \Delta u+u^{-\gamma} +g(u) = 0 in a bounded smooth domain \Omega \subset R^N with u = 0 on the boundary \partial \Omega, where \gamma > 1 and g is a smooth function. Assuming |g(t)| grows like t^{-\nu}, 0< \nu < \gamma, as t \rightarrow 0, we find optimal estimates of u(x) in terms of the distance of x from the boundary \partial \Omega.
Boundary estimates for solutions to singular elliptic equations
ANEDDA, CLAUDIA;CUCCU, FABRIZIO;
2005-01-01
Abstract
We deal with the Dirichlet problem \Delta u+u^{-\gamma} +g(u) = 0 in a bounded smooth domain \Omega \subset R^N with u = 0 on the boundary \partial \Omega, where \gamma > 1 and g is a smooth function. Assuming |g(t)| grows like t^{-\nu}, 0< \nu < \gamma, as t \rightarrow 0, we find optimal estimates of u(x) in terms of the distance of x from the boundary \partial \Omega.
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