Calculus of Variations and Geometric Measure Theory
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P. Baroni

Regularity in parabolic Dini continuous systems

created by baroni on 06 Oct 2012


Published Paper

Inserted: 6 oct 2012
Last Updated: 6 oct 2012

Journal: Forum Math.
Volume: 23
Number: 6
Pages: 1281-1322
Year: 2011


We consider a weak solution to the non-linear, parabolic systems $u_t-\text{div} \,A(x,t,u,Du)=0$, 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.


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