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arXiv · 2002.06076

Recovering a variable exponent

Tommi Brander·Jarkko Siltakoski
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Abstract

We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using a M\"untz-Sz\'asz theorem after reducing the problem to determining a function from its $L^p$-norms.

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Tommi Brander, Jarkko Siltakoski. 2020-02-14. Recovering a variable exponent. https://doi.org/10.25537/dm.2021v26.713-731

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