Geodesic
Recovering a variable exponent
Documenta mathematica, Tome 26 (2021), pp. 713-731.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 the properties of a moment problem after reducing the inverse problem to determining a function from its $L^p$-norms.
Classification : 34A55, 41A10, 34B15, 44A60, 28A25
Keywords: Calderón's problem, inverse problem, variable exponent, non-standard growth, Müntz-Szász theorem, approximation by polynomials, elliptic equation, quasilinear equation 
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     author = {Brander, Tommi and Siltakoski, Jarkko},
     title = {Recovering a variable exponent},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a37/}
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Brander, Tommi; Siltakoski, Jarkko. Recovering a variable exponent. Documenta mathematica, Tome 26 (2021), pp. 713-731. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a37/