Abstract We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group. On the basis of a generalization of the technique of 𝓐-harmonic approximation introduced by Duzaar-Grotowski-Kronz, and an appropriate Sobolev-Poincaré type inequality established in the Heisenberg group, we prove partial Hölder continuity results for vector-valued solutions of discontinuous sub-elliptic problems. The primary model covered by our analysis is the non-degenerate sub-elliptic p-Laplacian system with VMO-coefficients, involving sub-quadratic growth terms.

中文翻译：

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海森堡群中具有 VMO 系数的亚椭圆系统的正则性：亚二次结构情况

摘要 我们分别在海森堡群中，在可控生长条件和自然生长条件下，分别在 1 < p < 2 的情况下考虑具有 VMO 系数的非线性亚椭圆系统。在对 Duzaar-Grotowski-Kronz 引入的 𝓐-调和近似技术的推广，以及在 Heisenberg 群中建立的合适的 Sobolev-Poincaré 型不等式的基础上，我们证明了不连续子向量值解的部分 Hölder 连续性结果。 - 椭圆问题。我们的分析涵盖的主要模型是具有 VMO 系数的非退化亚椭圆 p-拉普拉斯系统，涉及亚二次增长项。