Erratum to Definition and properties of supersolutions to the porous medium equation (J. reine angew. Math. 618 (2008), 135–168)

Juha Kinnunen, Peter Lindqvist
2017 Journal für die Reine und Angewandte Mathematik  
Definition and properties of supersolutions to the porous medium equation (J. reine angew. Math. 618 (2008), 135-168) By Juha Kinnunen at Aalto and Peter Lindqvist at Trondheim It has come to our attention that an assumption is missing in Theorem 1.4 of our work [1]. The omission affects only the construction on page 157. The correction is to add the following assumption for the viscosity solution v W .0; T / ! . 1; 1: there does not exist a time t 0 , 0 < t 0 < T , such that lim If this
more » ... lim If this requirement is not fulfilled, it can be detected from the boundary behaviour, since then it must happen that lim sup .x; /!. ;t / v.x; / D 1 at some boundary point . ; t /, 2 , 0 < t < T . See [2]. References [1] J. Kinnunen and P. Lindqvist, Definition and properties of supersolutions to the porous medium equation, J. reine angew. Math. 618 (2008), 135-168. [2] J. Kinnunen and P. Lindqvist, Unbounded supersolutions of some quasilinear parabolic equations: A dichotomy, Nonlinear Anal. 131 (2016), 229-242.
doi:10.1515/crelle-2016-0002 fatcat:vhan32frtvdfjd45yo7d3ocpua