| Summary: | To calculate the parameters k in a stationary model Aku=ffrom measurements yˆof the solution u, i.e. to solve the inverse problem, usually a regularized minimization problem is solved and its solution kˆis considered as estimate of the true parameters. We focus on a situation which occurs e.g. for the coefficient functions k of a linear elliptic operator Aku=−divk∇uon a domain Ω⊂Rdand the total variation as regularization term. As functions k∈BV(Ω)of bounded variation can be discontinuous, existence of strong solutions u of Aku=fcannot be guaranteed and existence of minimizers cannot be obtained by standard methods. In this article, we prove solvability and stability for a general regularized minimization problem under weak assumptions, which particularly hold in case of BV(Ω)as parameter space due to a higher integrability result.
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