This paper identifies the free boundary arising in the two-dimensional monotone follower, cheap control problem It proves that if a region of inaction $mathcal{A}$ is of locally finite perimeter (LFP), then $mathcal{A}$ can be replaced by a new region of inaction $ ilde {mathcal{A}}$ whose boundary is locally $C^1 $ (up to sets of lower dimension). It then gives conditions under which the hypothesis (LFP) holds. Furthermore, under these conditions even higher regularity of the free boundary is obtained, namely $C^{2,alpha } $, except perhaps at a single corner point.
The Free Boundary of the Monotone Follower
Maria B. Chiarolla
;
1994-01-01
Abstract
This paper identifies the free boundary arising in the two-dimensional monotone follower, cheap control problem It proves that if a region of inaction $mathcal{A}$ is of locally finite perimeter (LFP), then $mathcal{A}$ can be replaced by a new region of inaction $ ilde {mathcal{A}}$ whose boundary is locally $C^1 $ (up to sets of lower dimension). It then gives conditions under which the hypothesis (LFP) holds. Furthermore, under these conditions even higher regularity of the free boundary is obtained, namely $C^{2,alpha } $, except perhaps at a single corner point.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
