TY  - JOUR
ID  - Vasilyev2019
LB  - Vasilyev2019
AU  - Vasilyev, Vladimir B.
TI  - Pseudo-differential equations and conical potentials: 2-dimensional case
ST  - Pseudo-differential equations and conical potentials: 2-dimensional case
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 1
SP  - 109
EP  - 124
DO  - https://doi.org/10.7494/OpMath.2019.39.1.109
UR  - https://doi.org/10.7494/OpMath.2019.39.1.109
AB  - We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
KW  - pseudo-differential equation
KW  - wave factorization
KW  - Dirichlet problem
KW  - system of linear integral equations
SN  - 1232-9274
ER  -