On the singularities of convex functions.
G. Alberti, L. Ambrosio, P. Cannarsa (1992)
Manuscripta mathematica
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G. Alberti, L. Ambrosio, P. Cannarsa (1992)
Manuscripta mathematica
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Yifeng Yu (2006)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In Albano-Cannarsa [1] the authors proved that, under some conditions, the singularities of the semiconcave viscosity solutions of the Hamilton-Jacobi equation propagate along generalized characteristics. In this note we will provide a simple proof of this interesting result.
Paolo Albano, Piermarco Cannarsa (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Zoltán M. Balogh, Matthieu Rickly (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We discuss differentiability properties of convex functions on Heisenberg groups. We show that the notions of horizontal convexity (h-convexity) and viscosity convexity (v-convexity) are equivalent and that h-convex functions are locally Lipschitz continuous. Finally we exhibit Weierstrass-type h-convex functions which are nowhere differentiable in the vertical direction on a dense set or on a Cantor set of vertical lines.
A. Fathi, M. Zavidovique (2010)
Rendiconti del Seminario Matematico della Università di Padova
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Ilia Bogaevski (1999)
Banach Center Publications
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We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphism. It turns out that the boundary of the convex hull is the front of a Legendre variety. Its singularities are classified up to contact diffeomorphism.
Patrick Bernard (2010)
Rendiconti del Seminario Matematico della Università di Padova
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