6533b7d1fe1ef96bd125d8f8
RESEARCH PRODUCT
Recovering a variable exponent
Tommi BranderJarkko Siltakoskisubject
non-standard growthvariable exponentelliptic equationGeneral Mathematicsquasilinear equationinversio-ongelmatCalderón's problemMathematics - Analysis of PDEsapproximation by polynomialsFOS: Mathematics34A55 (Primary) 41A10 34B15 28A25 (Secondary)inverse problemapproksimointiMüntz-Szász theoremdifferentiaaliyhtälötAnalysis of PDEs (math.AP)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-01-01 | Documenta Mathematica |