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September, 2011 Partial regularity for subquadratic parabolic systems by $\mathcal{A}$-caloric approximation
Christoph Scheven
Rev. Mat. Iberoamericana 27(3): 751-801 (September, 2011).


We establish a partial regularity result for weak solutions of nonsingular parabolic systems with subquadratic growth of the type $$ \partial_t u - \mathrm{div} a(x,t,u,Du) = B(x,t,u,Du), $$ where the structure function $a$ satisfies ellipticity and growth conditions with growth rate $\frac{2n}{n+2} < p < 2$. 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.


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Christoph Scheven . "Partial regularity for subquadratic parabolic systems by $\mathcal{A}$-caloric approximation." Rev. Mat. Iberoamericana 27 (3) 751 - 801, September, 2011.


Published: September, 2011
First available in Project Euclid: 9 August 2011

zbMATH: 1235.35061
MathSciNet: MR2895333

Primary: 35B65 , 35K40

Keywords: harmonic approximation , parabolic systems , partial regularity , singular set , subquadratic growth

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 3 • September, 2011
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