On Solvability Conditions for a Certain Conjugation Problem
Keyword(s):
We study a certain conjugation problem for a pair of elliptic pseudo-differential equations with homogeneous symbols inside and outside of a plane sector. The solution is sought in corresponding Sobolev–Slobodetskii spaces. Using the wave factorization concept for elliptic symbols, we derive a general solution of the conjugation problem. Adding some complementary conditions, we obtain a system of linear integral equations. If the symbols are homogeneous, then we can apply the Mellin transform to such a system to reduce it to a system of linear algebraic equations with respect to unknown functions.
1983 ◽
Vol 119
(1-2)
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pp. 101-142
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1972 ◽
Vol 37
(3)
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pp. 659-676
1977 ◽
Vol 11
(4)
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pp. 729-740
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Keyword(s):
2005 ◽
Vol 160
(2)
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pp. 579-587
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Keyword(s):
2019 ◽
Vol 38
(4)
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2018 ◽
Vol 20
(4)
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pp. 364-377