scholarly journals Partial regularity for sub-elliptic systems with Dini continuous coefficients involving natural growth terms in the Heisenberg group

2014 ◽  
Vol 412 (2) ◽  
pp. 828-840
Author(s):  
Dongni Liao ◽  
Jialin Wang ◽  
Zefeng Yu
Keyword(s):  
Heisenberg Group ◽  
Partial Regularity ◽  
Elliptic Systems ◽  
Natural Growth ◽  
Natural Growth Terms

scholarly journals Partial Hölder continuity for nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group

2018 ◽  
Vol 7 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Jialin Wang ◽  
Juan J. Manfredi
Keyword(s):  
Heisenberg Group ◽  
Weak Solutions ◽  
Hölder Continuity ◽  
Harmonic Approximation ◽  
Elliptic Systems ◽  
Natural Growth ◽  
Holder Continuity ◽  
Model Case ◽  
Horizontal Gradients ◽  
Vmo Coefficients

AbstractWe consider nonlinear sub-elliptic systems with VMO-coefficients in the Heisenberg group and prove partial Hölder continuity results for weak solutions using a generalization of the technique of {\mathcal{A}}-harmonic approximation. The model case is the following non-degenerate p-sub-Laplace system with super-quadratic natural growth with respect to the horizontal gradients Xu:-\sum_{i=1}^{2n}X_{i}\bigl{(}a(\xi\/)(1+|Xu|^{2})^{{(p-2)/2}}X_{i}u^{\alpha}% \bigr{)}=f^{\alpha},\quad\alpha=1,2,\ldots,N,where {a(\xi\/)\in\mathrm{VMO}} and {2<p<\infty}.

Partial regularity for discontinuous sub-elliptic systems with subquadratic growth in the Heisenberg group

2020 ◽  
Vol 195 ◽  
pp. 111719 ◽  
Author(s):  
Jialin Wang ◽  
Shuijin Zhang ◽  
Qiang Yang ◽  
Dongni Liao
Keyword(s):  
Heisenberg Group ◽  
Partial Regularity ◽  
Elliptic Systems
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