Boundary-Blow-Up Problems in a Fractal Domain

Assume that ci is a bounded domain in R" with N 2, which satisfies a uniform interior and exterior cone condition. We determine uniform a priori lower and upper bounds for the growth of solutions and their gradients, of the problem tu(x) = f(u(x)) (x e ci) with boundary blow-up, where 1(t) = e' or 1(t) = t P with p E (1,+oo). The boundary estimates imply existence and uniqueness of a solution of the above problem. For 1(t) = with p E (1,+oo) the solution is positive. These results are used to construct a solution of the problem when ci C R 2 is the von Koch snowflake domain.