L p Spectral Independence for Certain Uniformly Elliptic Operators

We consider certain self-adjoint uniformly elliptic operators of order 2 m acting on L P ( R N ) for values of p in the interval 1 ≤ p < ∞. The kind of problem which we consider has been treated fairly thoroughly for operators with smooth coefficients, [K, R], and we discuss instead the case in which all of the coefficients, including those of highest order, are bounded and measurable [D3]. The theory described below has been extended to a Riemannian manifold context in [D3], but we only describe the Euclidean version here. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.