# Gradient regularity for elliptic equations in the Heisenberg group

@inproceedings{Mingione2009GradientRF,
title={Gradient regularity for elliptic equations in the Heisenberg group},
author={Giuseppe Mingione and Anna Zatorska-Goldstein and Xiao Ling Zhong},
year={2009}
}
We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised in [40], where only dimension dependent bounds for the growth exponent are given. We also obtain explicit a priori local regularity estimates, and cover the case of the horizontal pLaplacean operator, extending some regularity proven in [17]. In turn, the a priori estimates found… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 38 REFERENCES

## Differentiability of solutions for the non-degenerate p-Laplacian in the Heisenberg group

VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

## Hypoelliptic second order differential equations

VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

## MINGIONE, Regularity results for quasilinear elliptic equations in the Heisenberg Group

G.J.J. MANFREDI
• Mathematische Annalen
• 2007
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

## Regularity of quasi-linear equations in the Heisenberg group

VIEW 12 EXCERPTS
HIGHLY INFLUENTIAL

## MINGIONE, Sharp regularity for functionals with (p, q)growth

L. ESPOSITO, G. F. LEONETTI
• J. Differential Equations
• 2004
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## MINGIONE, Regularity for minimizers of irregular integrals with (p, q)-growth

L. ESPOSITO, G. F. LEONETTI
• Forum Mathematicum
• 2002
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL

## $C^{1,\alpha}$ Local Regularity for the Solutions of the $p$-Laplacian on the Heisenberg Group for $2≤p VIEW 3 EXCERPTS HIGHLY INFLUENTIAL ## Regularity for quasilinear equations and$1-\$quasiconformal maps in Carnot groups

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

## Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL