The transmission problem with boundary conditions given by real measures

Dagmar Medková¹

¹ Department of Technical Mathematics Faculty of Mechanical Engineering Czech Technical University Karlovo nám. 13 12 135 Praha 2, Czech Republic

Annales Polonici Mathematici, Tome 92 (2007) no. 3, pp. 243-259.

Résumé

The unique solvability of the problem $\Delta u=0$ in $G^{+}\cup G^{-}$, $u_{+}-a{u}_{-}=f$ on $\partial G^{+}$, $n^{+}\cdot \mathrm{\nabla }{u}_{+}-b{n}^{+}\cdot \mathrm{\nabla }{u}_{-}=g$ on $\partial G^{+}$ is proved. Here $a$, $b$ are positive constants and $g$ is a real measure. The solution is constructed using the boundary integral equation method.

Détail

DOI : 10.4064/ap92-3-4

Mots-clés : unique solvability problem mit delta cup au partial cdot nabla bn cdot nabla partial proved here positive constants real measure solution constructed using boundary integral equation method