Schwartz-type boundary-value problems for canonical domains in a biharmonic plane

A commutative algebra \( \mathbbm{B} \) over the complex field with a basis {e1, e2} satisfying conditions {\left({e}_1^2+{e}_2^2\right)}^2=0,{e}_1^2+{e}_2^2\ne 0 is considered. This associated 2-D biharmonic equation. We consider Schwartz-type boundary-value problems on finding monogenic function of type Φ (xe1+ye2) = U1(x; y) e1 + U2(x; ie1 U3(x; e2 U4(x; ie2, (x; ∈ D, when values two components—either U1, U3 or U4—are given boundary domain D lying in Cartesian plane xOy. For solving those for half-plane and disk, we develop methods that are based solution expressions via integrals obtain solutions explicit form.