Asymptotic Dirichlet Problem for -Harmonic Functions on Manifolds with Pinched Curvature

作者：Heinonen Esko^*

来源：Potential Analysis, 2017, 46(1): 63-74.

DOI：10.1007/s11118-016-9569-7

• A-harmonic functions
• Dirichlet problem
• Hadamard manifold

We study the asymptotic Dirichlet problem for -harmonic functions on a Cartan-Hadamard manifold whose radial sectional curvatures outside a compact set satisfy an upper bound
and a pointwise pinching condition
for some constants epsilon > 0 and C (K) a 1, where P and are any 2-dimensional subspaces of T (x) M containing the (radial) vector acr(x) and r(x) = d(o, x) is the distance to a fixed point o a M. We solve the asymptotic Dirichlet problem with any continuous boundary data . The results apply also to the Laplacian and p-Laplacian, as special cases.

• 出版日期2017-1