On any complete Riemannian manifold M and for all p∈ [2 , ∞) , we prove a family of second-order L p -interpolation inequalities that arise from the following simple L p -estimate valid for every u∈ C ∞ (M) : ‖∇u‖pp≤‖uΔpu‖1∈[0,∞],where Δ p denotes the p-Laplace operator. We show that these inequalities, in combination with abstract functional analytic arguments, allow to establish new global Sobolev regularity results for L p -solutions of the Poisson equation for all p∈ (1 , ∞) , and new global Sobolev regularity results for the singular magnetic Schrödinger semigroups.

L-p-interpolation inequalities and global Sobolev regularity results (with an appendix by Ognjen Milatovic)

Pigola , Stefano
2019-01-01

Abstract

On any complete Riemannian manifold M and for all p∈ [2 , ∞) , we prove a family of second-order L p -interpolation inequalities that arise from the following simple L p -estimate valid for every u∈ C ∞ (M) : ‖∇u‖pp≤‖uΔpu‖1∈[0,∞],where Δ p denotes the p-Laplace operator. We show that these inequalities, in combination with abstract functional analytic arguments, allow to establish new global Sobolev regularity results for L p -solutions of the Poisson equation for all p∈ (1 , ∞) , and new global Sobolev regularity results for the singular magnetic Schrödinger semigroups.
2019
http://springerlink.metapress.com/app/home/journal.asp?wasp=cmw755wvtg0qvm8kjj1q&referrer=parent&backto=linkingpublicationresults,1:108198,1
Interpolation inequalities; Magnetic Schrödinger semigroups; Operator cores in L ; p; Poisson equation; Sobolev regularity;
Güneysu, Batu; Pigola, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2078329
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