Boundary value problems for third–order pseudoelliptic equations with degeneration

We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝⁿ, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x₁, …, x_n and B is a second-order elliptic operator acting in the same variables x₁, …, x_n. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s deriva-tives in the equation) are proved for the problems under study.