Strong unique continuation for the higher order fractional Laplacian
In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schrödinger operators. We deduce the strong unique continuation property in the presence of subcritical and critical Hardy type potentials. In the same setting, we address...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-01-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2019.4.715/fulltext.html |
| _version_ | 1811331183037906944 |
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| author | María Ángeles García-Ferrero Angkana Rüland |
| author_facet | María Ángeles García-Ferrero Angkana Rüland |
| author_sort | María Ángeles García-Ferrero |
| collection | DOAJ |
| description | In this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schrödinger operators. We deduce the strong unique continuation property in the presence of subcritical and critical Hardy type potentials. In the same setting, we address the unique continuation property from measurable sets of positive Lebesgue measure. As applications we prove the antilocality of the higher order fractional Laplacian and Runge type approximation theorems which have recently been exploited in the context of nonlocal Calderón type problems. As our main tools, we rely on the characterisation of the higher order fractional Laplacian through a generalised Caffarelli-Silvestre type extension problem and on adapted, iterated Carleman estimates. |
| first_indexed | 2024-04-13T16:15:18Z |
| format | Article |
| id | doaj.art-ea28d9abaa3b4e5c8696587859a0f021 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-04-13T16:15:18Z |
| publishDate | 2019-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-ea28d9abaa3b4e5c8696587859a0f0212022-12-22T02:40:05ZengAIMS PressMathematics in Engineering2640-35012019-01-011471577410.3934/mine.2019.4.715Strong unique continuation for the higher order fractional LaplacianMaría Ángeles García-Ferrero0Angkana Rüland1Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, GermanyMax-Planck-Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, GermanyIn this article we study the strong unique continuation property for solutions of higher order (variable coefficient) fractional Schrödinger operators. We deduce the strong unique continuation property in the presence of subcritical and critical Hardy type potentials. In the same setting, we address the unique continuation property from measurable sets of positive Lebesgue measure. As applications we prove the antilocality of the higher order fractional Laplacian and Runge type approximation theorems which have recently been exploited in the context of nonlocal Calderón type problems. As our main tools, we rely on the characterisation of the higher order fractional Laplacian through a generalised Caffarelli-Silvestre type extension problem and on adapted, iterated Carleman estimates.https://www.aimspress.com/article/10.3934/mine.2019.4.715/fulltext.htmlunique continuationfractional schrödinger equationhigher order nonlocal operatorscarleman estimates |
| spellingShingle | María Ángeles García-Ferrero Angkana Rüland Strong unique continuation for the higher order fractional Laplacian Mathematics in Engineering unique continuation fractional schrödinger equation higher order nonlocal operators carleman estimates |
| title | Strong unique continuation for the higher order fractional Laplacian |
| title_full | Strong unique continuation for the higher order fractional Laplacian |
| title_fullStr | Strong unique continuation for the higher order fractional Laplacian |
| title_full_unstemmed | Strong unique continuation for the higher order fractional Laplacian |
| title_short | Strong unique continuation for the higher order fractional Laplacian |
| title_sort | strong unique continuation for the higher order fractional laplacian |
| topic | unique continuation fractional schrödinger equation higher order nonlocal operators carleman estimates |
| url | https://www.aimspress.com/article/10.3934/mine.2019.4.715/fulltext.html |
| work_keys_str_mv | AT mariaangelesgarciaferrero stronguniquecontinuationforthehigherorderfractionallaplacian AT angkanaruland stronguniquecontinuationforthehigherorderfractionallaplacian |