Details

Autor(en) / Beteiligte

• Heinonen, Esko

Titel

Asymptotic Dirichlet Problem for ð" -Harmonic Functions on Manifolds with Pinched Curvature

Ist Teil von

• Potential analysis, 2017-01, Vol.46 (1), p.63-74

Ort / Verlag

Dordrecht: Springer Nature B.V

Erscheinungsjahr

2017

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the asymptotic Dirichlet problem for ð" -harmonic functions on a Cartan-Hadamard manifold whose radial sectional curvatures outside a compact set satisfy an upper bound K ( P ) ≤ − 1 + ε r ( x ) 2 log r ( x ) and a pointwise pinching condition | K ( P ) | ≤ C K | K ( P ′ ) | for some constants ε > 0 and CK ≥ 1, where P and P ′ are any 2-dimensional subspaces of TxM containing the (radial) vector ∇r(x) and r(x) = d(o, x) is the distance to a fixed point o ∈ M. We solve the asymptotic Dirichlet problem with any continuous boundary data f ∈ C ( ∂ ∞ M ) . The results apply also to the Laplacian and p-Laplacian, 1 < p < ∞ , as special cases.