Revista Matemática Iberoamericana

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

Christoph Scheven

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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.

Article information

Rev. Mat. Iberoamericana, Volume 27, Number 3 (2011), 751-801.

First available in Project Euclid: 9 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K40: Second-order parabolic systems 35B65: Smoothness and regularity of solutions

parabolic systems partial regularity harmonic approximation singular set subquadratic growth


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

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