Data di Pubblicazione:
2016
Citazione:
An extension problem for the fractional derivative defined by Marchaud / C. Bucur, F. Ferrari. - In: FRACTIONAL CALCULUS & APPLIED ANALYSIS. - ISSN 1311-0454. - 19:4(2016 Aug), pp. 867-887. [10.1515/fca-2016-0047]
Abstract:
We prove that the (nonlocal) Marchaud fractional derivative in R can be obtained from a parabolic extension problem with an extra (positive) variable as the operator that maps the heat conduction equation to the Neumann condition. Some properties of the fractional derivative are deduced from those of the local operator. In particular, we prove a Harnack inequality for Marchaud-stationary functions.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Marchaud derivative; fractional derivative; Harnack inequality, degenerate parabolic PDEs; extension problems
Elenco autori:
C. Bucur, F. Ferrari
Link alla scheda completa: