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  Volume 5, Issue 3, Article 70
 
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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