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Estimates for the $\partial-$Neumann Operator On Strongly Pseudo-Convex Domain With Lipschitz Boundary  
 
  Authors: S. Saber, O. Abdelkader,  
  Keywords: Sobolev estimate, Neumann problem, Lipschitz domains.  
  Date Received: 29/02/04  
  Date Accepted: 19/04/04  
  Subject Codes:

Primary 35N15; Secondary 32W05.

  
  Editors: Jozsef Sandor,  
 
  Abstract:

On a bounded strongly pseudo-convex domain $ X$ in $ mathbb{C}^{n}$ with a Lipschitz boundary, we prove that the $ bar{partial}-$Neumann operator $ N$ can be extended as a bounded operator from Sobolev $ (-1/2)-$spaces to the Sobolev $ (1/2)-$spaces. In particular, $ N$ is compact operator on Sobolev $ % (-1/2)-$spaces. ;


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