Elliptic extensions in the disk with operators in divergence form

Authors

  • O. Arena Università di Firenze
  • C. Giannotti Università di Camerino (Italy)

Keywords:

Elliptic equations in divergence form, Cauchy data

Abstract

Let $\varphi_0$ and $\varphi_1$ be regular functions on the boundary $\partial\disc$ of the unit disk $\disc$ in $\bR^2$, such that $\int_{0}^{2\pi}\varphi_1\,d\theta=0$ and $\int_{0}^{2\pi}\sin\theta(\varphi_1-\varphi_0)\,d\theta=0$. It is proved that there exist a linear second order uniformly elliptic operator $L$ in divergence form with bounded measurable coefficients and a function $u$ in $W^{1,p}(D)$, $1 < p <2$, such that $Lu=0$ in $\disc$ and with $\left.u\right|_{\partial\disc}= \varphi_0$ and the conormal derivative $\left.\frac{\partial u}{\partial N}\right|_{\partial\disc}=\varphi_1$. 10.1017/S000497271200069X

Author Biographies

O. Arena, Università di Firenze

Dipartimento di Costruzioni e Restauro Full Professor

C. Giannotti, Università di Camerino (Italy)

Scuola di Scienze e Tecnologie Research assistant

Published

2013-07-23

Issue

Vol. 88 No. 1 (2013)

Section

Articles
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