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arXiv · 1808.04168

Variable exponent Calder\'on's problem in one dimension

Tommi Brander·David Winterrose
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Abstract

We consider one-dimensional Calder\'on's problem for the variable exponent $p(\cdot)$-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 $p(\cdot)$-Laplace equation from Dirichlet and Neumann data of solutions. We give a constructive and local uniqueness proof for conductivities in $L^\infty$ restricted to the coarsest sigma-algebra that makes the exponent $p(\cdot)$ measurable.

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Tommi Brander, David Winterrose. 2018-08-13. Variable exponent Calder\'on's problem in one dimension. https://doi.org/10.5186/aasfm.2019.4459

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