The unique solvability of the problem Δu = 0 in G⁺ ∪ G¯, u₊ - au_ = f on ∂G⁺, n⁺·∇u₊ - bn⁺·∇u_ = g on ∂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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-3-4,
author = {Dagmar Medkov\'a},
title = {The transmission problem with boundary conditions given by real measures},
journal = {Annales Polonici Mathematici},
volume = {92},
year = {2007},
pages = {243-259},
zbl = {1149.35026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-3-4}
}
Dagmar Medková. The transmission problem with boundary conditions given by real measures. Annales Polonici Mathematici, Tome 92 (2007) pp. 243-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-3-4/