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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 23, Issue 6


Regularity in parabolic Dini continuous systems

Paolo Baroni
Published Online: 2010-06-27 | DOI: https://doi.org/10.1515/form.2011.049


We consider a weak solution to the non-linear, parabolic systems of the form

ut – div A(x, t, u, Du) = 0,

where the vector field A satisfies a Dini-type continuity condition with respect to the variables (x, t, u), and we prove a partial regularity result for such a solution. Moreover, we give an estimate of the size of the singular set of a solution in terms of a generalized parabolic Hausdorff measure associated to an appropriate modulus of continuity naturally associated to the coefficients of the system.

Keywords.: Partial regularity; parabolic systems; Dini continuity

About the article

Received: 2009-10-13

Revised: 2010-02-21

Published Online: 2010-06-27

Published in Print: 2011-11-01

Citation Information: Forum Mathematicum, Volume 23, Issue 6, Pages 1281–1322, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.049.

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