Abstract
Lavrentiev’s theorem provides bounds for analytic functions known to be small at a finite number of points in a bounded region. An analogous result is established for solutions of elliptic equations on bounded regions in ℝ2 and applied to estimating non-uniqueness error in elliptic inverse problems.
Mathematics Subject Classification (2010). 35R30, 35J25, 86A22.
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Knowles, I., LaRussa, M.A. (2012). Lavrentiev’s Theorem and Error Estimation in Elliptic Inverse Problems. In: Brown, B., Lang, J., Wood, I. (eds) Spectral Theory, Function Spaces and Inequalities. Operator Theory: Advances and Applications(), vol 219. Springer, Basel. https://doi.org/10.1007/978-3-0348-0263-5_6
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DOI: https://doi.org/10.1007/978-3-0348-0263-5_6
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