A unique-continuation principle for sums of fractional Laplacians is proved on Euclidean space and applied to recover anisotropic coefficients and potentials in fractional polyharmonic equations.
A Calder\'on type inverse problem for the active scalar equations with fractional dissipation
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abstract
In this paper, we are interested in an inverse problem for the active scalar equations with fractional dissipation on the torus. We perform a second order linearization to relate our model to the linear fractional diffusion equation. Our approach to solving the inverse problem relies on nonlocal phenomena such as the unique continuation property of the fractional Laplacian and its associated Runge approximation property. A remarkable feature of our model is that the divergence-free structure in the nonlinear term plays an important role in both forward and inverse problems.
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2024 1verdicts
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Entanglement principle for the fractional Laplacian with applications to inverse problems
A unique-continuation principle for sums of fractional Laplacians is proved on Euclidean space and applied to recover anisotropic coefficients and potentials in fractional polyharmonic equations.