Explicit solution of the jump problem for the Laplace equation and singularities at the edges
2001 ◽
Vol 7
(1)
◽
pp. 1-13
◽
Keyword(s):
The boundary value problem for the Laplace equation outside several cuts in a plane is studied. The jump of the solution of the Laplace equation and the jump of its normal derivative are specified on the cuts. The problem is studied under different conditions at infinity, which lead to different uniqueness and existence theorems. The solution of this problem is constructed in the explicit form by means of single layer and angular potentials. The singularities at the ends of the cuts are investigated.
2012 ◽
Vol 2012
◽
pp. 1-12
◽
Keyword(s):
2019 ◽
Vol 22
(3)
◽
pp. 104-113
2016 ◽
Vol 24
(6)
◽
2020 ◽
pp. 114-126
1995 ◽
Vol 18
(4)
◽
pp. 705-710
◽
1981 ◽
Vol 3
(1)
◽
pp. 38-69
◽
2009 ◽
Vol 57
(2)
◽
pp. 135-148