0370680 - MÚ 2012 RIV US eng J - Journal Article
Medková, Dagmar
Transmission problem for the Laplace equation and the integral equation method.
Journal of Mathematical Analysis and Applications. Roč. 387, č. 2 (2012), s. 837-843. ISSN 0022-247X. E-ISSN 1096-0813
Institutional research plan: CEZ:AV0Z10190503
Keywords : transmission problem * Laplace equation * boundary integral equation
Subject RIV: BA - General Mathematics
Impact factor: 1.050, year: 2012
http://www.sciencedirect.com/science/article/pii/S0022247X11008985

We shall study a weak solution in the Sobolev space of the transmission problem for the Laplace equation using the integral equation method. First we use the indirect integral equation method. We look for a solution in the form of the sum of the double layer potential corresponding to the skip of traces on the interface and a single layer potential with an unknown density. We get an integral equation on the boundary. We prove that this equation has a form (I + M)phi = F where M is a contractive operator. So, we can obtain a solution of this equation using the successive approximation method. Moreover, we are able to estimate the norm of the operator M and control how quickly this process converges. Then we study the direct integral equation method. We obtain the same integral equation like for the indirect integral equation method. So, we can again calculate a solution using the successive approximation method.
Permanent Link: http://hdl.handle.net/11104/0204405