Assume that is a bounded domain in with , 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 with boundary blow-up, where or with . The boundary estimates imply existence and uniqueness of a solution of the above problem. For with the solution is positive. These results are used to construct a solution of the problem when is the von Koch snowflake domain.
Cite this article
J. Matero, Boundary-Blow-Up Problems in a Fractal Domain. Z. Anal. Anwend. 15 (1996), no. 2, pp. 419–444DOI 10.4171/ZAA/708