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9 papers found.
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Optimal partial regularity of very weak solutions to nonhomogeneous A-harmonic systems

We study partial regularity of very weak solutions to some nonhomogeneous A-harmonic systems. To obtain the reverse Hölder inequality of the gradient of a very weak solution, we construct a suitable test function by Hodge decomposition. With the aid of Gehring’s lemma, we prove that these very weak solutions are weak solutions. Further, we show that these solutions are in fact ...

Regularity theory on A-harmonic system and A-Dirac system

In this paper, we show the regularity theory on an A-harmonic system and an A-Dirac system. By the method of the removability theorem, we explain how an A-harmonic system arises from an A-Dirac system and establish that an A-harmonic system is in fact the real part of the corresponding A-Dirac system.

Boundary regularity for quasilinear elliptic systems with super quadratic controllable growth condition

We consider the boundary regularity for weak solutions to quasilinear elliptic systems under a super quadratic controllable growth condition, and we obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. Combined with existing results on the interior partial regularity, this result yields an upper bound on the Hausdorff dimension ...

A-Harmonic operator in the Dirac system

In this paper, we show how an A-harmonic operator arises from A-Dirac systems under natural growth condition. By the method of removable singularities for solutions to A-Dirac systems with natural growth conditions, we establish the fact that A-harmonic equations are the real part of the corresponding A-Dirac systems.

The relation between A-harmonic operator and A-Dirac system

In this paper, we show how an A-harmonic operator arises from Dirac systems under controllable growth condition. By the method of removable singularities for solutions to the A-Dirac system with controllable growth conditions, we establish the fact that an A-harmonic operator is a real part of the corresponding A-Dirac systems.

Optimal partial regularity of second-order parabolic systems under natural growth condition

We consider the regularity for weak solutions of second-order nonlinear parabolic systems under a natural growth condition when m > 2 , and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione.

Boundary regularity for elliptic systems with supquadratic growth

We consider boundary regularity for weak solutions of quasilinear elliptic systems with the supquadratic growth condition and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. By an element covering argument combined with existing interior partial regularity results, we establish the boundary regularity result.

Boundary regularity result for quasilinear elliptic systems

’ contributions Shuhong Chen participated in design of the study and drafted the manuscript. Zhong Tan participated in conceived of the study and the amendment of the paper. All authors read and approved the final

Optimal Interior Partial Regularity for Nonlinear Elliptic Systems for the Case under Natural Growth Condition

We consider the interior regularity for weak solutions of second-order nonlinear elliptic systems with subquadratic growth under natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particularly the regularity we obtained is optimal.