Abstract
We consider certain self-adjoint uniformly elliptic operators of order 2m 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.
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Davies, E.B. (1996). L p Spectral Independence for Certain Uniformly Elliptic Operators. In: Hörmander, L., Melin, A. (eds) Partial Differential Equations and Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 21. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0775-7_7
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DOI: https://doi.org/10.1007/978-1-4612-0775-7_7
Publisher Name: Birkhäuser, Boston, MA
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