Hausdorff Dimension of Ruptures for Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity
نویسندگان
چکیده
We consider the following semilinear elliptic equation with singular nonlinearity: u ? 1 u + h(x) = 0 in where > 1; h(x) 2 C 1 (() and is an open subset in R n ; n 2. Let u 2 C 0 (() be a nonnegative nite energy stationary solution and = fx 2 ju(x) = 0g be the rupture set of u. We show that the Hausdorr dimension of is less than or equal to (n?2)+(n+2) +1 .
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