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On the fractional powers of a Schrödinger operator with a Hardy-type potential

Part of: Elliptic equations and systems Miscellaneous topics - Partial differential equations Partial differential equations

Published online by Cambridge University Press:  12 April 2024

Giovanni Siclari Open the ORCID record for Giovanni Siclari [Opens in a new window]
Giovanni Siclari*
Affiliation:
Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano – Bicocca, Milano, Italy (g.siclari2@campus.unimib.it)
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Abstract

Strong unique continuation properties and a classification of the asymptotic profiles are established for the fractional powers of a Schrödinger operator with a Hardy-type potential, by means of an Almgren monotonicity formula combined with a blow-up analysis.

Keywords

fractional elliptic equationsunique continuationmonotonicity formulaHardy-type potentials

MSC classification

Primary: 35R11: Fractional partial differential equations 35J75: Singular elliptic equations 35B40: Asymptotic behavior of solutions 35B60: Continuation and prolongation of solutions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 67 , Issue 2 , May 2024 , pp. 460 - 507
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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