We investigate blow-up solutions of the equation \Delta u = u^p + g(u) in a bounded smooth domain \Omega. If p > 1 and if g satisfies appropriate growth conditions (compared with the growth of t^p) as t goes to infinity we find optimal asymptotic estimates of the solution u(x) in terms of the distance of x from the boundary \partial \Omega.
Higher order boundary estimates for blow-up solutions of elliptic equations
ANEDDA, CLAUDIA;
2006-01-01
Abstract
We investigate blow-up solutions of the equation \Delta u = u^p + g(u) in a bounded smooth domain \Omega. If p > 1 and if g satisfies appropriate growth conditions (compared with the growth of t^p) as t goes to infinity we find optimal asymptotic estimates of the solution u(x) in terms of the distance of x from the boundary \partial \Omega.
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