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| PARTIAL REGULARITY RESULT OF SUPERQUADRATIC ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS |
| Yalin Qiu |
| (anks{Corresponding author. E-mail: qylfjly@163.com School of Math. and Computing Science, Longyan University, Longyan 364012, Fujian, PR China) |
| DOI： |
| 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 А-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 H?lder exponent for the derivative of the weak solutions on the regular set. |
| Key words: superquadratic elliptic systems; controllable growth condition; А-harmonic approximation; optimal partial regularity |