JournalsrmiVol. 27, No. 3pp. 751–801

Partial regularity for subquadratic parabolic systems by A\mathcal{A}-caloric approximation

  • Christoph Scheven

    Friedrich-Alexander-Universität Erlangen, Germany
Partial regularity for subquadratic parabolic systems by $\mathcal{A}$-caloric approximation cover
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Abstract

We establish a partial regularity result for weak solutions of nonsingular parabolic systems with subquadratic growth of the type

tudiva(x,t,u,Du)=B(x,t,u,Du),\partial_t u - \mathrm{div} a(x,t,u,Du) = B(x,t,u,Du),

where the structure function aa satisfies ellipticity and growth conditions with growth rate 2nn+2<p<2\frac{2n}{n+2} < p < 2. We prove Hölder continuity of the spatial gradient of solutions away from a negligible set. The proof is based on a variant of a harmonic type approximation lemma adapted to parabolic systems with subquadratic growth.

Cite this article

Christoph Scheven, Partial regularity for subquadratic parabolic systems by A\mathcal{A}-caloric approximation. Rev. Mat. Iberoam. 27 (2011), no. 3, pp. 751–801

DOI 10.4171/RMI/652