JournalszaaVol. 12, No. 2pp. 327–341

Identifiability of the Transmissivity Coefficient in an Elliptic Boundary Value Problem

  • Gennadi Vainikko

    Tartu University, Estonia
  • Karl Kunisch

    Karl-Franzens-Universität Graz, Austria
Identifiability of the Transmissivity Coefficient in an Elliptic Boundary Value Problem cover
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Abstract

We deal with a coefficient inverse problem describing the filtration of ground water in a region ΩRn,n2\Omega \subset R^n, n ≥ 2. Introducing a weak formulation of the problem, discretization and regularization methods can be constructed in a natural way. These methods converge to the normal solution of the problem, i.e. to a transmissivity coefficient of a minimal L2(Ω)L^2 (\Omega)-norm. Thus a question about L2L^2-identifiability (identifiability among functions of the class L2(Ω)L^2 (\Omega) of the transmissivity coefficient arises. Our purpose is to describe subregions of Ω\Omega where the transmissivity coefficient is really L2L^2-identifiable or even L1L^1-identifiable. Thereby we succeed introducing physically realistic conditions on the data of the problem, e.g. piecewise smooth surfaces in Ω\Omega are allowed where the data of the inverse problem may have discontinuities. With some natural changes, our results about the L1L^1-identifiability extend known results about the identifiability among more smooth functions given by G. R. Richter [4], C. Chicone and J. Gerlach [1], and K. Kunisch [3].

Cite this article

Gennadi Vainikko, Karl Kunisch, Identifiability of the Transmissivity Coefficient in an Elliptic Boundary Value Problem. Z. Anal. Anwend. 12 (1993), no. 2, pp. 327–341

DOI 10.4171/ZAA/562