Boundary value problem with normal derivatives for a higher-order elliptic equation on the plane

On the Schwarz Problem for the Moisil–teodorescu System in a Spherical Layer and in the Interior of a Torus

“…In [17][18][19] works questions of the Fredholm solvability of the Neumann problem for a higher order elliptic equation on the plane were studied, and the equivalence of the solvability condition for the generalized Neumann problem with the complementary condition (the Shapiro-Lopatinsky condition) was proved.…”

Dirichlet and Neumann Boundary Value Problems for the Polyharmonic Equation in the Unit Ball

“…where the polynomials h m,k (λ) are defined in (17). Using (24), the polynomial h m,k (λ) can be written in the form…”

“…The solvability of various Neumann-type problems and their generalizations in the unit ball for the biharmonic and polyharmonic equation are analyzed in [14][15][16]. In [17], for the boundary value problems for the polyharmonic equation with normal derivatives in the boundary conditions, the sufficient condition for these problems to be Fredholm is obtained, and a formula for their index is given.…”

Solvability of Boundary Value Problems With Non-Local Conditions for Multidimensional Hyperbolic Equations

“…The problems of finding solvability conditions for boundary value problems for a polyharmonic equation in a ball were investigated in [19]. In [20], for derivatives of the l 2 -th order equation with constant (and only higher) real coefficients, normal derivatives were studied under boundary conditions. For these problems, sufficient conditions for the Fredholm solvability of the problem are obtained and formulas for the index of the problem are given.…”