### Abstract

We consider one-dimensional Calderón's problem for the variable exponent p(·)-Laplace equation and find out that more can be seen than in the constant exponent case. The problem is to recover an unknown weight (conductivity) in the weighted p(·)-Laplace equation from Dirichlet and Neumann data of solutions. We give a constructive and local uniqueness proof for conductivities in L

^{∞}restricted to the coarsest sigma-algebra that makes the exponent p(·) measurable.Original language | English |
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Journal | Annales Academiae Scientiarum Fennicae. Mathematica |

Volume | 44 |

Pages (from-to) | 925-943 |

ISSN | 1239-629X |

DOIs | |

Publication status | Published - 2019 |

### Keywords

- Calderón's problem
- Inverse problem
- Variable exponent
- Non-standard growth
- Elliptic equation
- Quasilinear equation