Journal of the European Mathematical Society

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Volume 18, Issue 12, 2016, pp. 2953–2969
DOI: 10.4171/JEMS/658

Published online: 2016-11-21

Perron's method for the porous medium equation

Juha Kinnunen[1], Peter Lindqvist[2] and Teemu Lukkari[3]

(1) Aalto University, Finland
(2) Norwegian University of Science and Technology, Trondheim, Norway
(3) Aalto University, Finland

This work extends Perron’s method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.

Keywords: Perron method, Porous medium equation, comparison principle, obstacles

Kinnunen Juha, Lindqvist Peter, Lukkari Teemu: Perron's method for the porous medium equation. J. Eur. Math. Soc. 18 (2016), 2953-2969. doi: 10.4171/JEMS/658