Abstract. Having given weightρ = ρ (dist(x,∂ Q)) defined on cube Q and Orlicz function R , we construct the weight ω ρ (·,·) defined on ∂ Q×∂ Q and extension operator Ext

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Abstract. Having a given weight ρ(x) = τ (dist(x,∂ Ω)) defined on Lipschitz boundary domain Ω and an Orlicz function Ψ , we construct the subordinated weight ω(·,·) defined on ∂ Ω × ∂ Ω and extension operator Ext

We prove the existence and uniqueness of solution to the nonhomogeneous degenerate elliptic PDE of second order with boundary data in weighted Orlicz-Slobodetskii space. Our goal is to consider the possibly general assumptions on the involved constraints: the class of weights, the boundary data, and the admitted coefficients. We also provide some estimates on the spectrum of our degenerate elliptic operator. KEYWORDS boundary value problems, degenerate elliptic PDEs, upper and lower bounds of eigenvalues, weighted Slobodetskii spaces, weighted Sobolev spaces 544