A relationship between the Dirichlet and Regularity Problems for elliptic equations

Zhongwei Shen

A relationship between the Dirichlet and Regularity Problems for elliptic equations

偏微分方程分析 2007-05-23 v1

作者: Zhongwei Shen

摘要

We study the relationship between the solvability of the $L^p$ Dirichlet problem $(D)_p$ and that of the $L^q$ regularity problem $(R)_q$ for second order elliptic equations with bounded measurable coefficients. It is known that the solvability of $(R)_p$ implies that of $(D)_{p^\prime}$ . In this note we show that if $(D)_{p^\prime}$ is solvable, then either $(R)_p$ is solvable or $(R)_q$ is not solvable for any $1<q<\infty$ .

关键词

regularity for elliptic equations dirichlet problem elliptic partial differential equations

引用

@article{arxiv.math/0607239,
  title  = {A relationship between the Dirichlet and Regularity Problems for elliptic equations},
  author = {Zhongwei Shen},
  journal= {arXiv preprint arXiv:math/0607239},
  year   = {2007}
}

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