The fractional p -biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems

Autor: Manas Kar, Jesse Railo, Philipp Zimmermann
Přispěvatelé: Kar, Manas [0000-0001-6036-1535], Railo, Jesse [0000-0001-9226-4190], Zimmermann, Philipp [0000-0002-6791-1779], Apollo - University of Cambridge Repository
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Calculus of Variations and Partial Differential Equations, 62 (4)
ISSN: 0944-2669
1432-0835
Popis: This article investigates nonlocal, quasilinear generalizations of the classical biharmonic operator (- Δ) 2. These fractional p -biharmonic operators appear naturally in the variational characterization of the optimal fractional Poincaré constants in Bessel potential spaces. We study the following basic questions for anisotropic fractional p -biharmonic systems: existence and uniqueness of weak solutions to the associated interior source and exterior value problems, unique continuation properties, monotonicity relations, and inverse problems for the exterior Dirichlet-to-Neumann maps. Furthermore, we show the UCP for the fractional Laplacian in all Bessel potential spaces Ht,p for any t∈ R, 1 ≤ p< ∞ and s∈ R+\ N: If u∈ Ht,p(Rn) satisfies (- Δ) su= u= 0 in a nonempty open set V, then u≡ 0 in Rn. This property of the fractional Laplacian is then used to obtain a UCP for the fractional p -biharmonic systems and plays a central role in the analysis of the associated inverse problems. Our proofs use variational methods and the Caffarelli–Silvestre extension.
Calculus of Variations and Partial Differential Equations, 62 (4)
ISSN:0944-2669
ISSN:1432-0835
Databáze: OpenAIRE
Externí odkaz: