Dirichlet finite biharmonic functions on the plane with distorted metrics
Mitsuru Nakai · Nagoya Mathematical Journal · 1973
The Laplace-Beltrami operator Δ on a smooth manifold M with a smooth Riemannian metric ds2 = ∑i,jgij(x)dxidxj applied to a smooth function φ takes the form Functions in the class H2(M) = {u∈ C4(M); Δ2u = 0} are called biharmonic.