Functional calculi of second-order elliptic partial differential operators with bounded measurable coefficients |
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Authors: | Xuan Thinh Duong Alan McIntosh |
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Institution: | 1. School of Mathematics, Physics, Computing and Electronics, Macquarie University, NSW 2109, Australia
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Abstract: | Consider a second-order elliptic partial differential operatorL in divergence form with real, symmetric, bounded measurable coefficients, under Dirichlet or Neumann conditions on the boundary of a strongly Lipschitz domain Ω. Suppose that 1 <p < ∞ and μ > 0. ThenL has a bounded H∞ functional calculus in Lp(Ω), in the sense that ¦¦f (L +cI)u¦¦p ≤C sup¦arλ¦<μ ¦f¦ ¦‖u¦‖p for some constantsc andC, and all bounded holomorphic functionsf on the sector ¦ argλ¦ < μ that contains the spectrum ofL +cI. We prove this by showing that the operatorsf(L + cI) are Calderón-Zygmund singular integral operators. |
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