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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/434211
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