Complex Neumann type boundary problem and decomposition of Lebesgue spaces

Pages: 201 - 210, Volume 10, Issue 1/2, January/February 2004

doi:10.3934/dcds.2004.10.201       Abstract        Full Text (148.5K)       Related Articles

Julii A. Dubinskii - Moscow Power Engineering Institute, Moscow, Russian Federation (email)

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.

Keywords:  Complex Neumann problem, decomposition of Lebesgue spaces, Poincaré's inequality.
Mathematics Subject Classification:  30E25.

Received: May 2003;      Revised: September 2003;      Published: October 2003.