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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 2, 1998, pp. 431–441
DOI: 10.4171/ZAA/831

Published online: 1998-06-30

Blow-Up in Exterior Domains: Existence and Star-Shapedness

E. Francini[1] and Antonio Greco[2]

(1) CNR, Firenze, Italy
(2) Università degli Studi di Cagliari, Italy

For some nonlinear elliptic equations in divergence form, we consider the solutions, defined in the exterior of a contractible bounded domain $\mathcal G$, which become infinite at the boundary. We prove the existence of such solutions and study the shape of their level sets when $\mathcal G$ is star-shaped.

Keywords: Contractible domains, elliptic equations, maximum and comparison principles

Francini E., Greco Antonio: Blow-Up in Exterior Domains: Existence and Star-Shapedness. Z. Anal. Anwend. 17 (1998), 431-441. doi: 10.4171/ZAA/831