The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (1453 KB) | Metadata | Table of Contents | ZAA summary
Volume 15, Issue 2, 1996, pp. 419–444
DOI: 10.4171/ZAA/708

Published online: 1996-06-30

Boundary-Blow-Up Problems in a Fractal Domain

J. Matero[1]

(1) Uppsala Universitet, Sweden

Assume that $\Omega$ is a bounded domain in $\mathbb R^N$ 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 $\Delta u(x) = f(u(x)) (x \in \Omega)$ with boundary blow-up, where $f(t) = e^t$ or $f(t) = t^p$ with $p \in (1,+\infty)$. The boundary estimates imply existence and uniqueness of a solution of the above problem. For $f(t) = t^p$ with $p \in (1,+\infty)$ the solution is positive. These results are used to construct a solution of the problem when $\Omega \subset \mathbb R^2$ is the von Koch snowflake domain.

Keywords: Blow-up, snowflake, fractaLe, gradient estimates

Matero J.: Boundary-Blow-Up Problems in a Fractal Domain. Z. Anal. Anwend. 15 (1996), 419-444. doi: 10.4171/ZAA/708