Sharp boundedness and continuity results for the singular porous medium equation

Bögelein V, Duzaar F, Gianazza U (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Israel Journal of Mathematics Springer Verlag (Germany)

Book Volume: 214

Pages Range: 259--314

Journal Issue: 1

DOI: 10.1007/s11856-016-1360-3

Abstract

We consider non-homogeneous, singular (0 < m < 1) parabolic equations of porous medium type of the form ut−divA(x,t,u,Du)=μinET, where E T is a space time cylinder, and µ is a Radon-measure having finite total mass µ(E T ). In the range (N−2)+N < m < 1 we establish sufficient conditions for the boundedness and the continuity of u in terms of a natural Riesz potential of the right-hand side measure µ.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Università degli Studi di Pavia IT Italy (IT) Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT)

How to cite

APA:

Bögelein, V., Duzaar, F., & Gianazza, U. (2016). Sharp boundedness and continuity results for the singular porous medium equation. Israel Journal of Mathematics, 214(1), 259--314. https://dx.doi.org/10.1007/s11856-016-1360-3

MLA:

Bögelein, Verena, Frank Duzaar, and Ugo Gianazza. "Sharp boundedness and continuity results for the singular porous medium equation." Israel Journal of Mathematics 214.1 (2016): 259--314.

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