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An Inverse Problem for a Quasilinear Elliptic Equation

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We consider the inverse problem for a quasilinear second order elliptic equation with the unknown coefficient at the lower-order term and the first kind boundary condition and the integral overedetermination condition on the boundary. We prove a theorem on the local existence and uniqueness of a strong solution to the problem. The result is illustrated by an example of a nonlinear equation satisfying all the assumptions of the theorem.

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Authors and Affiliations

  1. Siberian Federal University, 79, Svobodny, Krasnoyarsk, 660041, Russia

    A. Sh. Lyubanova & A. V. Velisevich

Authors
  1. A. Sh. Lyubanova
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  2. A. V. Velisevich
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Correspondence to A. Sh. Lyubanova.

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Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 79-85.

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Lyubanova, A.S., Velisevich, A.V. An Inverse Problem for a Quasilinear Elliptic Equation. J Math Sci 270, 591–599 (2023). https://doi.org/10.1007/s10958-023-06370-9

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  • DOI: https://doi.org/10.1007/s10958-023-06370-9

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