English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove a unique continuation property for the fractional Laplacian$(-\Delta)^s$ when $s \in (-n/2,\infty)\setminus \mathbb{Z}$. In addition, westudy Poincar\'e-type inequalities for the operator $(-\Delta)^s$ when $s\geq0$. We apply the results to show that one can uniquely recover, up to a gauge,electric and magnetic potentials from the Dirichlet-to-Neumann map associatedto the higher order fractional magnetic Schr\"odinger equation. We also studythe higher order fractional Schr\"odinger equation with singular electricpotential. In both cases, we obtain a Runge approximation property for theequation. Furthermore, we prove a uniqueness result for a partial data problemof the $d$-plane Radon transform in low regularity. Our work extends somerecent results in inverse problems for more general operators.

Unique continuation property and Poincar\'e inequality for higher order fractional Laplacians with applications in inverse problems