An operator theoretical approach of some inverse problems
Abstract
This work gives an overview of the solution to linear forward and inverse problems for a class of elliptic partial differential equations in two-dimensional domains Ω, in the framework of Banach spaces and operators. We focus on the equation ∇(σ∇u) = 0, with σ in Sobolev spaces W 1,p(Ω), 1 < p < ∞, with Dirichlet or Neumann or mixed boundary conditions. For domains Ω with Dini-smooth boundary ∂Ω, the approach is based on the properties of generalized Hardy spaces.
Domains
Mathematics [math]
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