Minimization problems for Lipschitz functions via viscosity solutions
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Convex functions on Carnot groups
Juutinen, Petri; Lu, Guozhen; Manfredi, Juan; Stroffolini, Bianca (European Mathematical Society Publishing House, 2007)We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point ... -
Density of Lipschitz functions in energy
Eriksson-Bique, Sylvester (Springer Science and Business Media LLC, 2023)In this paper, we show that the density in energy of Lipschitz functions in a Sobolev space N1,p(X) holds for all p∈[1,∞) whenever the space X is complete and separable and the measure is Radon and positive and finite on ... -
Lipschitz Functions on Submanifolds of Heisenberg Groups
Julia, Antoine; Nicolussi Golo, Sebastiano; Vittone, Davide (Oxford University Press (OUP), 2023)We study the behavior of Lipschitz functions on intrinsic C1 submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusin-type ... -
Yet another proof of the density in energy of Lipschitz functions
Lučić, Danka; Pasqualetto, Enrico (Springer, 2024)We provide a new, short proof of the density in energy of Lipschitz functions into the metric Sobolev space defined by using plans with barycenter (and thus, a fortiori, into the Newtonian–Sobolev space). Our result covers ... -
Solving some optimal control problems using the Barrier penalty function method
Neittaanmäki, Pekka; Stachurski, Andrzej (Springer, 1992)In this paper we present a new approach to solve a two-level optimization problem arising from an approximation by means of the finite element method of optimal control problems governed by unilateral boundary-value problems. ...