{"paper":{"title":"On some properties of solutions of the $p$-harmonic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"SH. Chen, S. Ponnusamy, X. Wang","submitted_at":"2012-04-12T16:35:01Z","abstract_excerpt":"A $2p$-times continuously differentiable complex-valued function $f=u+iv$ in a simply connected domain $\\Omega\\subseteq\\mathbb{C}$ is \\textit{p-harmonic} if $f$ satisfies the $p$-harmonic equation $\\Delta ^pf=0.$ In this paper, we investigate the properties of $p$-harmonic mappings in the unit disk $|z|<1$. First, we discuss the convexity, the starlikeness and the region of variability of some classes of $p$-harmonic mappings. Then we prove the existence of Landau constant for the class of functions of the form $Df=zf_{z}-\\barzf_{\\barz}$, where $f$ is $p$-harmonic in $|z|<1$. Also, we discuss "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2767","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}