TY - JOUR
T1 - Partial Regularity Result of Superquadratic Elliptic Systems with Dini Continuous Coefficients
AU - Qiu , Yalin
JO - Annals of Applied Mathematics
VL - 2
SP - 162
EP - 185
PY - 2022
DA - 2022/06
SN - 33
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20603.html
KW - superquadratic elliptic systems, controllable growth condition,
$\mathcal{A}$-harmonic approximation, optimal partial regularity.
AB - <p style="text-align: justify;">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.</p>