We study a class of upper semicontinuous functions $f:\mathbb R^d\to\mathbb R$ whose hypograph $\mathrm{hypo}\,f$ satisfies a geometric regularity property, namely: there exist $c>0$, $\theta\in]0,1]$ such that for each $P$ on the boundary of $\mathrm{hypo}\,f$ there exists a unitary Fr\'echet (outer) normal $v\in N^F_{\mathrm{hypo}\,f}(P)\cap\mathbb S^d$ to $\mathrm{hypo}\,f$ with \[\langle v,P-Q\rangle\le c \|P-Q\|^{1+\theta}\qquad\textrm{for every }Q\in\mathrm{hypo}\,f.\]

BV Regularity and Differentiability Properties of a Class of Upper Semicontinuous Functions

MARIGONDA, ANTONIO;
2014-01-01

Abstract

We study a class of upper semicontinuous functions $f:\mathbb R^d\to\mathbb R$ whose hypograph $\mathrm{hypo}\,f$ satisfies a geometric regularity property, namely: there exist $c>0$, $\theta\in]0,1]$ such that for each $P$ on the boundary of $\mathrm{hypo}\,f$ there exists a unitary Fr\'echet (outer) normal $v\in N^F_{\mathrm{hypo}\,f}(P)\cap\mathbb S^d$ to $\mathrm{hypo}\,f$ with \[\langle v,P-Q\rangle\le c \|P-Q\|^{1+\theta}\qquad\textrm{for every }Q\in\mathrm{hypo}\,f.\]
2014
9783662438800
nonsmooth analysis; Geometric measure theory; Frechet normals
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/749561
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