$C^{1,\alpha}$ Local Regularity for the Solutions of the $p$-Laplacian on the Heisenberg Group for $2≤p<1+\sqrt5$

Silvana Marchi

doi:10.4171/zaa/1035

$C^{1, α}$ Local Regularity for the Solutions of the $p$ -Laplacian on the Heisenberg Group for $2 \leq p < 1 + 5$

Silvana Marchi
Università di Parma, Italy

$$C^{1,\alpha}$ Local Regularity for the Solutions of the $p$-Laplacian on the Heisenberg Group for $2≤p<1+\sqrt5$ cover$

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Abstract

We prove local Hölder continuity of the homogeneous gradient for weak solutions $u \in W_{l oc}^{1, p}$ of the $p$ -Laplacian on the Heisenberg group $H^{n}$ for $2 \leq p < 1 + 5$ .

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Cite this article

Silvana Marchi, $C^{1, α}$ Local Regularity for the Solutions of the $p$ -Laplacian on the Heisenberg Group for $2 \leq p < 1 + 5$ . Z. Anal. Anwend. 20 (2001), no. 3, pp. 617–636

DOI 10.4171/ZAA/1035