Partial and full regularity for restricted classes of \(p\)-harmonic maps. (English) Zbl 0849.58020
A map \(u : B^3 \to S^2\) is axially symmetric if \(u : (r, \theta, z) \mapsto (\theta, \psi (r,z))\). The \(p\)-energy, for \(2 < p < 3\), has the form \(E_p (u) = \int_{B^3} |\nabla u |^pd\)vol. Estimates of the Hausdorff dimension of the singular set of a map minimizing the \(p\)-energy among axially symmetric maps are received. The existence of a large class of axially symmetric boundary data (including surjective data) whose members admit regular \(p\)-harmonic extensions is demonstrated.
Reviewer: V.Pavlenko (Chelyabinsk)
MSC:
| 58E20 | Harmonic maps, etc. |
| 58J32 | Boundary value problems on manifolds |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
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