Year: 2017
Author: Yalin Qiu
Annals of Applied Mathematics, Vol. 33 (2017), Iss. 2 : pp. 162–185
Abstract
We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of $\mathcal{A}$-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal Hölder exponent for the derivative of the weak solutions on the regular set.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-AAM-20603
Annals of Applied Mathematics, Vol. 33 (2017), Iss. 2 : pp. 162–185
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: superquadratic elliptic systems controllable growth condition $\mathcal{A}$-harmonic approximation optimal partial regularity.