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L^p resolvent estimates for variable coefficient elliptic systems on Lipschitz domains

Wei Wei

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China

Current address: School of Mathematics, Northwest University, Xi'an 710127, P. R. China.

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and

Zhenqiu Zhang

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China

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https://doi.org/10.1142/S021953051450050XCited by:5 (Source: Crossref)

Abstract

In this paper, we treat the general strongly elliptic systems with a class of singular potentials on a bounded Lipschitz domain Ω ⊂ ℝ^d, d ≥ 3. We establish the L^p resolvent estimates on Ω for the above systems with vanishing Dirichlet type or Neumann type boundary value condition, where 2d/(d + 2) - ϵ < p < 2d/(d - 2) + ϵ with some positive constant ϵ = ϵ(Ω).

Keywords:

AMSC: 35J47, 35J57, 47A10

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