Abstract
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.
Highlights
Published: 20 September 2021The theory of pseudo-differential equations on manifolds with a smooth boundary was systematically developed, starting from the papers of M.I
This paper is related to this approach, and it is devoted to some generalizations of classical results for the Riemann boundary value problem [12,13] in which we consider model pseudo-differential equations in canonical non-smooth domains instead of the Cauchy–Riemann operator
These studies were indicated in [14], and here we develop these results, obtaining more exact and refined solvability conditions
Summary
The theory of pseudo-differential equations on manifolds with a smooth boundary was systematically developed, starting from the papers of M.I. This paper is related to this approach, and it is devoted to some generalizations of classical results for the Riemann boundary value problem [12,13] in which we consider model pseudo-differential equations in canonical non-smooth domains instead of the Cauchy–Riemann operator. These studies were indicated in [14], and here we develop these results, obtaining more exact and refined solvability conditions. The Mellin transform [15] is used to reduce the problem for homogeneous elliptic symbols to the mentioned algebraic system
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