We study a linear elliptic partial differential equation of second order in a bounded domain ? ? R N , with nonstandard boundary conditions on a part ? of the boundary ??. Here, neither the solution nor its normal derivative are prescribed pointwise. Instead, the average of the solution over ? is given and the normal derivative along ? has to follow a prescribed shape function, apart from an additive (unknown) constant. We prove the well-posedness of the problem and provide a method for the recovery of the unknown boundary data.
@article{611,
title = {Recovery of the boundary data for a linear second order elliptic problem
with a nonlocal boundary condition},
journal = {ANZIAM Journal},
volume = {42},
year = {2000},
doi = {10.21914/anziamj.v42i0.611},
language = {EN},
url = {http://dml.mathdoc.fr/item/611}
}
Schepper, Hennie De; Slodivcka, Marian. Recovery of the boundary data for a linear second order elliptic problem with a nonlocal boundary condition. ANZIAM Journal, Tome 42 (2000) . doi : 10.21914/anziamj.v42i0.611. http://gdmltest.u-ga.fr/item/611/