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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 3, 2001, pp. 617–636
DOI: 10.4171/ZAA/1035

Published online: 2001-09-30

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

Silvana Marchi[1]

(1) Università di Parma, Italy

We prove local Hölder continuity of the homogeneous gradient for weak solutions $u \in W^{1,p}_{loc}$ of the $p$-Laplacian on the Heisenberg group $\mathbb H^n$ for $2≤p<1+\sqrt 5$.

Keywords: Degenerate elliptic equations, weak solutions, regularity of solutions, higher differentiability

Marchi Silvana: $C^{1,\alpha}$ Local Regularity for the Solutions of the $p$-Laplacian on the Heisenberg Group for $2≤p<1+\sqrt5$. Z. Anal. Anwend. 20 (2001), 617-636. doi: 10.4171/ZAA/1035