The Robin Function and Its Eigenvalues
Keyword(s):
Abstract The paper deals with the Robin function and eigenvalue problems generated by the Robin operator. First we show that Green's function of an 𝑛-fold connected domain is the Robin function of an appropriate simply connected domain. The main part of the paper deals with eigenvalue problems for the Robin operator: the mixed Stekloff eigenvalue problem and the membrane problem with mixed boundary conditions. Isoperimetric inequalities are proved for the sum of reciprocal eigenvalues.
1953 ◽
Vol 5
(3-4)
◽
pp. 269-294
◽
1984 ◽
Vol 36
(2)
◽
pp. 175-183
◽
Keyword(s):
1958 ◽
Vol 64
(2)
◽
pp. 45-56
◽
1982 ◽
Vol 22
(3)
◽
pp. 165-172
◽
1977 ◽
Vol 29
(2)
◽
pp. 111-118
◽
Keyword(s):
1989 ◽
Vol 32
(1)
◽
pp. 107-119
◽
Keyword(s):
1989 ◽
Vol 34
(9)
◽
pp. 986-990
◽