scholarly journals Lp resolvent estimates for constant coefficient elliptic systems on Lipschitz domains

2014 ◽  
Vol 267 (9) ◽  
pp. 3262-3293 ◽  
Author(s):  
Wei Wei ◽  
Zhenqiu Zhang
Keyword(s):  
Constant Coefficient ◽  
Elliptic Systems ◽  
Lipschitz Domains ◽  
Resolvent Estimates

Lp resolvent estimates for variable coefficient elliptic systems on Lipschitz domains

2015 ◽  
Vol 13 (06) ◽  
pp. 591-609 ◽  
Author(s):  
Wei Wei ◽  
Zhenqiu Zhang
Keyword(s):  
Positive Constant ◽  
Lipschitz Domain ◽  
Variable Coefficient ◽  
Elliptic Systems ◽  
Lipschitz Domains ◽  
Singular Potentials ◽  
Resolvent Estimates ◽  
Bounded Lipschitz Domain ◽  
Neumann Type ◽  
Type Boundary

In this paper, we treat the general strongly elliptic systems with a class of singular potentials on a bounded Lipschitz domain Ω ⊂ ℝd, d ≥ 3. We establish the Lp 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).

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