Estimates in Morrey Spaces and Hölder Continuity for Weak Solutions to Degenerate Elliptic Systems

2011 ◽  
Vol 138 (3-4) ◽  
pp. 419-437 ◽  
Author(s):  
Yan Dong ◽  
Pengcheng Niu
Keyword(s):  
Weak Solutions ◽  
Hölder Continuity ◽  
Elliptic Systems ◽  
Morrey Spaces ◽  
Holder Continuity ◽  
Degenerate Elliptic

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 A Note on Regularity of Solutions to Degenerate Elliptic Equations of Caffarelli-Kohn-Nirenberg Type

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Veronica Felli ◽  
Matthias Schneider
Keyword(s):  
Weak Solutions ◽  
Elliptic Equations ◽  
Hölder Continuity ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Holder Continuity ◽  
Degenerate Elliptic

AbstractWe establish Hölder continuity of weak solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type.

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