# Regularity results for quasilinear elliptic equations in the Heisenberg group

@article{Manfredi2007RegularityRF,
title={Regularity results for quasilinear elliptic equations in the Heisenberg group},
author={Juan J. Manfredi and Giuseppe Mingione},
journal={Mathematische Annalen},
year={2007},
volume={339},
pages={485-544}
}
We prove regularity results for solutions to a class of quasilinear elliptic equations in divergence form in the Heisenberg group $${\mathbb{H}}^n$$ . The model case is the non-degenerate p-Laplacean operator $$\sum_{i=1}^{2n} X_i \left( \left(\mu^2+ \left| {\mathfrak{X}}u \right|^2\right)^\frac{p-2}{2} X_i u\right) =0,$$ where $$\mu > 0$$ , and p is not too far from 2.
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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 29 REFERENCES

## Multiple integrals in the calculus of variations

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

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

VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

## Regularity for quasilinear equations and $1-$quasiconformal maps in Carnot groups

VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

## An embedding theorem and the harnack inequality for nonlinear subelliptic equations

VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

## Direct Methods in the Calculus of Variations

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Hypoelliptic second order differential equations

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

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

VIEW 13 EXCERPTS
HIGHLY INFLUENTIAL

## Doctoral dissertation

L. Capogna
• Purdue University,
• 1996
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

VIEW 1 EXCERPT

## J

A. Domoko
• J. Manfredi, C-regularity for p-harmonic functions in the Heisenberg group for p near 2. In “The p-Harmonic Equation and Recent Advances in Analysis”, ed. P. Poggi-Corradini, Contemporary Mathematics 370, American Mathematical Society,
• 2005
VIEW 1 EXCERPT