An Lp-Comparison, $p\in (1,\infty )$, on the Finite Differences of a Discrete Harmonic Function at the Boundary of a Discrete Box
An Lp-Comparison, $p\in (1,\infty )$, on the Finite Differences of a Discrete Harmonic Function at the Boundary of a Discrete Box
Abstract It is well-known that for a harmonic function u defined on the unit ball of the d -dimensional Euclidean space, d ≥ 2, the tangential and normal component of the gradient ∇ u on the sphere are comparable by means of the L p -norms, $p\in (1,\infty )$ <mml:math …