Geodesic
Recovering a variable exponent
Documenta mathematica, Tome 26 (2021), pp. 713-731 Cet article a éte moissonné depuis la source EMS Press

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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 Lp-norms.
DOI : 10.4171/dm/827
Classification : 28A25, 34A55, 34B15, 41A10, 44A60
Mots-clés : inverse problem, Calderón's problem, variable exponent, non-standard growth, Müntz-Szász theorem, approximation by polynomials, elliptic equation, quasilinear equation 
@article{10_4171_dm_827,
     author = {Tommi Brander and Jarkko Siltakoski},
     title = {Recovering a variable exponent},
     journal = {Documenta mathematica},
     pages = {713--731},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/827},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/827/}
}
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Tommi Brander; Jarkko Siltakoski. Recovering a variable exponent. Documenta mathematica, Tome 26 (2021), pp. 713-731. doi: 10.4171/dm/827

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