Abstract
We consider the Dirichlet boundary value problem for higher order elliptic equations in divergence form with discontinuous coefficients in polyhedral angles. Some uniqueness results are proved.
Highlights
1 Introduction The Dirichlet problem for the polyharmonic equation in a bounded domain of Rn has been studied by Sobolev in [ ]
In [ ], the author obtains the uniqueness of the solution of the Dirichlet problem
- for every l ∈ {, . . . , n – }, Rnl = x = (x, x, . . . , xn) ∈ Rn : xi >, i = n – l, . . . , n is the ‘polyhedral angle’ with vertex in the origin; - for l = the above definition gives the half-space Rn+; - for ρ > we denote by Qρ = {x ∈ Rnl : |x| < ρ}
Summary
The Dirichlet problem for the polyharmonic equation in a bounded domain of Rn has been studied by Sobolev in [ ]. In [ ], the author obtains the uniqueness of the solution of the Dirichlet problem,. We are concerned with the following Dirichlet problem for a homogeneous equation in divergence form of order m:. ). Our main results consist in two uniqueness theorems obtained for some particular cases of problem The main tool in our analysis is a generalization of the Hardy inequality proved by Kondrat’ev and Oleinik in [ ] (see Section )
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