Variable exponent Calderón's problem in one dimension

Tommi Olavi Brander, David Scott Winterrose*

*Corresponding author for this work

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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.
Original languageEnglish
JournalAnnales Academiae Scientiarum Fennicae. Mathematica
Volume44
Pages (from-to)925-943
ISSN1239-629X
DOIs
Publication statusPublished - 2019

Keywords

  • Calderón's problem
  • Inverse problem
  • Variable exponent
  • Non-standard growth
  • Elliptic equation
  • Quasilinear equation

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