Solvability of a fourth order elliptic problem in a bounded sector, part I

The purpose of this article (composed of two parts) is the study of the generalized dispersal operator of a reaction-diffusion equation in L^p -spaces set in the finite conical domain S_ω ,ρ of angle ω >0 and radius ρ >0 in ℝ^2 . This first part is devoted to the behavior of the solution near the top of the cone which is completely described in the weighted Sobolev space W^4,p_3-1/p(S_ω ,ρ _0) , ρ _0 ⩽ρ , see Theorem 2.2 .