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Volume 14, Issue 1
Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains

Henggeng Wang & Houyu Jia

J. Part. Diff. Eq., 14 (2001), pp. 1-11.

Published online: 2001-02

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  • Abstract
In this paper, firstly we give an atomic decomposition of the local Hardy spaces h^p_r(Ω)(O < p ≤ 1) and their dual spaces. where the domain Ω is exterior regular in R^n(n ≥ 3). Then for given data f ∈ h^p_r(Ω), we discuss the inhomogeneous Dirichlet problems: {Lu = f \quad in Ω u = 0 \qquad on ∂ Ω where the operator L is uniformly elliptic. Also we obtain the estimation of Green potential in the local Hardy spaces h^p_r(Ω).
  • Keywords

Exterior regular domain local Hardy space Hölder space inhomogeneous Dirichlet problem Green potential

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@Article{JPDE-14-1, author = {}, title = {Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {1}, pages = {1--11}, abstract = { In this paper, firstly we give an atomic decomposition of the local Hardy spaces h^p_r(Ω)(O < p ≤ 1) and their dual spaces. where the domain Ω is exterior regular in R^n(n ≥ 3). Then for given data f ∈ h^p_r(Ω), we discuss the inhomogeneous Dirichlet problems: {Lu = f \quad in Ω u = 0 \qquad on ∂ Ω where the operator L is uniformly elliptic. Also we obtain the estimation of Green potential in the local Hardy spaces h^p_r(Ω).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5464.html} }
TY - JOUR T1 - Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 11 PY - 2001 DA - 2001/02 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5464.html KW - Exterior regular domain KW - local Hardy space KW - Hölder space KW - inhomogeneous Dirichlet problem KW - Green potential AB - In this paper, firstly we give an atomic decomposition of the local Hardy spaces h^p_r(Ω)(O < p ≤ 1) and their dual spaces. where the domain Ω is exterior regular in R^n(n ≥ 3). Then for given data f ∈ h^p_r(Ω), we discuss the inhomogeneous Dirichlet problems: {Lu = f \quad in Ω u = 0 \qquad on ∂ Ω where the operator L is uniformly elliptic. Also we obtain the estimation of Green potential in the local Hardy spaces h^p_r(Ω).
Henggeng Wang & Houyu Jia . (2019). Local Hardy Spaces and Inhomogeneous Dirichlet Problems in Exterior Regular Domains. Journal of Partial Differential Equations. 14 (1). 1-11. doi:
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