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February  2004, 10(1&2): 201-210. doi: 10.3934/dcds.2004.10.201

Complex Neumann type boundary problem and decomposition of Lebesgue spaces

Julii A. Dubinskii 1,

1. 

Moscow Power Engineering Institute, Moscow, Russian Federation

Received  May 2003 Revised  September 2003 Published  October 2003

In this article, we study the generalization of the the decomposition $W_p^m(G)=\mathcal O_p^m(G)\oplus\partial W_{p,0}^{m+1}(G), p>1,m=0,\pm 1,\cdots$ to the case of several complex variables. More precisely, we consider the Lebesgue space $L_2(G)$ and prove that the above decomposition is closely related to the solvability of a complex Neumann problem whose solvability is equivalent to the complex version of Poincaré's inequality.
Keywords: Poincaré's inequality., decomposition of Lebesgue spaces, Complex Neumann problem.
Mathematics Subject Classification: 30E2.
Citation: Julii A. Dubinskii. Complex Neumann type boundary problem and decomposition of Lebesgue spaces. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 201-210. doi: 10.3934/dcds.2004.10.201
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