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International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 36, Issue 1


A variable exponent Sobolev theorem for fractional integrals on quasimetric measure spaces

Stefan Samko
  • Corresponding author
  • Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, 8005-139 Faro, Portugal
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Published Online: 2015-08-27 | DOI: https://doi.org/10.1515/anly-2015-5003


We prove that the coefficients aij(x), q(x) and the domain Ω of a multidimensional fractional diffusion equation can be recovered uniquely from measurements u(b,t), t(t0,t1), at an arbitrary single point b inside a bounded domain Ωn. From the measurements we first recover infinitely many spectral data (λm,ϕm(x)) of the elliptic operator associated with the fractional diffusion equation. Then, the coefficients aij(x) and q(x) are found from linear algebraic systems of the form Ay=b, where A is a generalized Wronskian of some set of eigenfunctions that can be shown to be nontrivial. The domain Ω is reconstructed using the first eigenfunction ϕ1(x).

Keywords: Variable exponent spaces; Sobolev type theorem; fractional integrals; quasimetric measure spaces

MSC: 46E30; 26A33; 31A05

About the article

Received: 2015-04-01

Accepted: 2015-07-09

Published Online: 2015-08-27

Published in Print: 2016-02-01

Funding Source: Russian Fund of Basic Research

Award identifier / Grant number: 15-01-02732

Citation Information: Analysis, Volume 36, Issue 1, Pages 27–37, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1515/anly-2015-5003.

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