Morrey estimates for a class of noncoercive elliptic systems with VMO-coefficients

2021 ◽  
Vol 32 (2) ◽  
pp. 317-334
Author(s):  
Giuseppa Rita Cirmi ◽  
Salvatore D’Asero ◽  
Salvatore Leonardi
Keyword(s):  
Elliptic Systems ◽  
Morrey Estimates ◽  
Vmo Coefficients

scholarly journals $L^p$ estimates for degenerate elliptic systems with VMO coefficients

2014 ◽  
Vol 25 (6) ◽  
pp. 909-917
Author(s):  
G. Di Fazio ◽  
M. S. Fanciullo ◽  
P. Zamboni
Keyword(s):  
Elliptic Systems ◽  
Degenerate Elliptic ◽  
Vmo Coefficients

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}.

scholarly journals Parabolic and Elliptic Systems with VMO Coefficients

2009 ◽  
Vol 16 (3) ◽  
pp. 365-388 ◽  
Author(s):  
Hongjie Dong ◽  
Doyoon Kim
Keyword(s):  
Elliptic Systems ◽  
Vmo Coefficients

scholarly journals Regularity for sub-elliptic systems with VMO-coefficients in the Heisenberg group: the sub-quadratic structure case

2020 ◽  
Vol 10 (1) ◽  
pp. 420-449
Author(s):  
Jialin Wang ◽  
Maochun Zhu ◽  
Shujin Gao ◽  
Dongni Liao
Keyword(s):  
Heisenberg Group ◽  
Harmonic Approximation ◽  
Type Inequality ◽  
Elliptic Systems ◽  
Growth Conditions ◽  
Quadratic Growth ◽  
Primary Model ◽  
Vmo Coefficients ◽  
Controllable Growth ◽  
Vector Valued

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.

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