A Relationship Between the Dirichlet and Regularity Problems for Elliptic Equations

• Autores: Zhongwei Shen
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 2, 2007, págs. 205-213
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n2.a4
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• Resumen

  • Let $\Cal{L}=\text{div}A\nabla$ be a real, symmetric second order elliptic operator with bounded measurable coefficients. Consider the elliptic equation $\Cal{L}u=0$ in a bounded Lipschitz domain $\Omega$ of $\Bbb{R}^n$. We study the relationship between the solvability of the $L^p$ Dirichlet problem $(D)_p$ with boundary data in $L^p(\partial \Omega)$ and that of the $L^q$ regularity problem $(R)_q$ with boundary data in $W^{1,q}(\partial \Omega)$, where $1