Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 925-943

VARIABLE EXPONENT CALDERÓN'S PROBLEM IN ONE DIMENSION

Tommi Brander and David Winterrose

Technical University of Denmark, Department of Applied Mathematics and Computer Science
Richard Petersens Plads 324, DK-2800 Kgs. Lyngby, Denmark; tommi.brander 'at' ntno.no

Technical University of Denmark, Department of Applied Mathematics and Computer Science
Richard Petersens Plads 324, DK-2800 Kgs. Lyngby, Denmark; dawin 'at' dtu.dk

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.

2010 Mathematics Subject Classification: Primary 35R30; Secondary 34A55, 35J92, 35J62, 35J70, 46N20, 34B15.

Key words: Calderón's problem, inverse problem, variable exponent, non-standard growth, elliptic equation, quasilinear equation.

Reference to this article: T. Brander and D. Winterrose: Variable exponent Calderón's problem in one dimension. Ann. Acad. Sci. Fenn. Math. 44 (2019), 925-943.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4459