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Regularity in parabolic Dini continuous systems.
- Source :
-
Forum Mathematicum . 2011, Vol. 23 Issue 6, p1281-1322. 42p. - Publication Year :
- 2011
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09337741
- Volume :
- 23
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 67291931
- Full Text :
- https://doi.org/10.1515/FORM.2011.049