Let Ω ⊂ R^N be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary ∂Ω on the behavior of the blow-up solution to the equation Δu = u^p|∇u|^q. Under appropriate conditions on p and q, we find asymptotic expansions up to the second order of the solution u in terms of the distance from x to the boundary ∂Ω.
Second order estimates for boundary blowup solutions of quasilinear elliptic equations
MARRAS, MONICA;
2015-01-01
Abstract
Let Ω ⊂ R^N be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary ∂Ω on the behavior of the blow-up solution to the equation Δu = u^p|∇u|^q. Under appropriate conditions on p and q, we find asymptotic expansions up to the second order of the solution u in terms of the distance from x to the boundary ∂Ω.
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