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Book Sections Year : 2023

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.
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hal-04355468 , version 1 (20-12-2023)

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Juliette Leblond, Elodie Pozzi. An operator theoretical approach of some inverse problems. Ilia Binder; Damir Kinzebulatov; Javad Mashreghi. Function Spaces, Theory and Applications, Springer, In press, Fields Institute Communications ; vol 87, 978-3-031-39272-6. ⟨10.1007/978-3-031-39270-2_3⟩. ⟨hal-04355468⟩
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