A stability estimate for an elliptic problem (Q1769173)

The authors deal with the Cauchy problem for linear elliptic operators with \(C^\infty\)-coefficients at a regular domain \(\mathbb{D}\subset\mathbb{R}^n\). More precisely, they consider solutions of the Cauchy problem of the form \[ a_1 A_2u= 0\quad\text{in }\Omega,\tag{1} \] \[ \partial^j_v u= g_j\quad\text{on }\Gamma,\quad j= 0,1,2,3,\tag{2} \] where \(A_1\), \(A_2\) are second-order elliptic operators and \(\Gamma\) is a part of \(\partial\Omega\) which is open in \(\partial\Omega\). The purpose of the paper is to present a stability estimate for the solution of (1)--(2).