Trace Hardy inequality for the Euclidean space with a cut and its applications

0542656 - ÚJF 2022 RIV US eng J - Článek v odborném periodiku
Dauge, M. - Jex, M. - Lotoreichik, Vladimir
Trace Hardy inequality for the Euclidean space with a cut and its applications.
Journal of Mathematical Analysis and Applications. Roč. 500, č. 2 (2021), č. článku 125124. ISSN 0022-247X. E-ISSN 1096-0813
Grant CEP: GA ČR(CZ) GA21-07129S
Institucionální podpora: RVO:61389005
Klíčová slova: Trace Hardy inequality * Jump of the trace * non-closed cut * heat equation * delta'-interaction
Obor OECD: Pure mathematics
Impakt faktor: 1.417, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jmaa.2021.125124

We obtain a trace Hardy inequality for the Euclidean space with a bounded cut Sigma subset of R-d, d >= 2. In this novel geometric setting, the Hardy-type inequality nontypically holds also for d = 2. The respective Hardy weight is given in terms of the geodesic distance to the boundary of Sigma. We provide its applications to the heat equation on R-d with an insulating cut at Sigma and to the Schrodinger operator with a delta'-interaction supported on Sigma. We also obtain generalizations of this trace Hardy inequality for a class of unbounded cuts.
Trvalý link: http://hdl.handle.net/11104/0320029