Complex Neumann type boundary problem and decomposition of Lebesgue spaces

Julii A. Dubinskii

doi:10.3934/dcds.2004.10.201

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2004, Volume 10, Issue 1&2: 201-210. Doi: 10.3934/dcds.2004.10.201

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Complex Neumann type boundary problem and decomposition of Lebesgue spaces

Julii A. Dubinskii^1,

1.
Moscow Power Engineering Institute, Moscow

Received: May 2003

Revised: September 2003

Published: January 2004

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Abstract

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.

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Mathematics Subject Classification: 30E25.

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