Complex Neumann type boundary problem and decomposition of Lebesgue spaces

Previous Article
Positivity for large time of solutions of the heat equation: the parabolic antimaximum principle
DCDS Home
This Issue
Next Article
Uniform exponential attractors for a singularly perturbed damped wave equation

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

Complex Neumann type boundary problem and decomposition of Lebesgue spaces

1.	Moscow Power Engineering Institute, Moscow, Russian Federation

Received May 2003 Revised September 2003 Published October 2003

Abstract
Related Papers

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

[1]	Dirk Pauly. On Maxwell's and Poincaré's constants. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 607-618. doi: 10.3934/dcdss.2015.8.607
[2]	Markus Banagl. Singular spaces and generalized Poincaré complexes. Electronic Research Announcements, 2009, 16: 63-73. doi: 10.3934/era.2009.16.63
[3]	Alexander Moreto. Complex group algebras of finite groups: Brauer's Problem 1. Electronic Research Announcements, 2005, 11: 34-39.
[4]	Ferdinand Verhulst. Henri Poincaré's neglected ideas. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 1-17. doi: 10.3934/dcdss.2020079
[5]	Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011
[6]	Antonio Giorgilli, Stefano Marmi. Convergence radius in the Poincaré-Siegel problem. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 601-621. doi: 10.3934/dcdss.2010.3.601
[7]	Felipe Riquelme. Ruelle's inequality in negative curvature. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2809-2825. doi: 10.3934/dcds.2018119
[8]	S. S. Dragomir, C. E. M. Pearce. Jensen's inequality for quasiconvex functions. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 279-291. doi: 10.3934/naco.2012.2.279
[9]	Shengliang Pan, Deyan Zhang, Zhongjun Chao. A generalization of the Blaschke-Lebesgue problem to a kind of convex domains. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1587-1601. doi: 10.3934/dcdsb.2016012
[10]	Keonhee Lee, Ngoc-Thach Nguyen, Yinong Yang. Topological stability and spectral decomposition for homeomorphisms on noncompact spaces. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2487-2503. doi: 10.3934/dcds.2018103
[11]	Joseph J Kohn. Nirenberg's contributions to complex analysis. Discrete & Continuous Dynamical Systems - A, 2011, 30 (2) : 537-545. doi: 10.3934/dcds.2011.30.537
[12]	Giuseppe Geymonat, Françoise Krasucki. Hodge decomposition for symmetric matrix fields and the elasticity complex in Lipschitz domains. Communications on Pure & Applied Analysis, 2009, 8 (1) : 295-309. doi: 10.3934/cpaa.2009.8.295
[13]	Chao Deng, Tong Li. Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 183-195. doi: 10.3934/dcdsb.2018093
[14]	Hartmut Pecher. The Chern-Simons-Higgs and the Chern-Simons-Dirac equations in Fourier-Lebesgue spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (8) : 4875-4893. doi: 10.3934/dcds.2019199
[15]	Neal Bez, Sanghyuk Lee, Shohei Nakamura, Yoshihiro Sawano. Sharpness of the Brascamp–Lieb inequality in Lorentz spaces. Electronic Research Announcements, 2017, 24: 53-63. doi: 10.3934/era.2017.24.006
[16]	Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153
[17]	Kevin Arfi, Anna Rozanova-Pierrat. Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d-sets. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 1-26. doi: 10.3934/dcdss.2019001
[18]	Jussi Behrndt, A. F. M. ter Elst. The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 661-671. doi: 10.3934/dcdss.2017033
[19]	Daniel Guan. Classification of compact complex homogeneous spaces with invariant volumes. Electronic Research Announcements, 1997, 3: 90-92.
[20]	Fang Zeng, Pablo Suarez, Jiguang Sun. A decomposition method for an interior inverse scattering problem. Inverse Problems & Imaging, 2013, 7 (1) : 291-303. doi: 10.3934/ipi.2013.7.291

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences