Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590048 | Journal of Functional Analysis | 2014 | 46 Pages |
Abstract
We consider parabolic equations of porous medium type of the formut−divA(x,t,u,Du)=μinET, in some space time cylinder ETET. The most prominent example covered by our assumptions is the classical porous medium equationut−Δum=μinET, with m≥1m≥1. We establish a sufficient condition for the continuity of u in terms of a natural Riesz potential of the right-hand side measure μ. As an application we come up with a borderline condition ensuring the continuity of u : more precisely, if μ∈L(N+22,1), then u is continuous in ETET.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Verena Bögelein, Frank Duzaar, Ugo Gianazza,