Author:
Ambrosio Luigi,Brena Camillo,Conti Sergio
Abstract
AbstractIn this paper we analyze in detail a few questions related to the theory of functions with bounded p-Hessian–Schatten total variation, which are relevant in connection with the theory of inverse problems and machine learning. We prove an optimal density result, relative to the p-Hessian–Schatten total variation, of continuous piecewise linear (CPWL) functions in any space dimension d, using a construction based on a mesh whose local orientation is adapted to the function to be approximated. We show that not all extremal functions with respect to the p-Hessian–Schatten total variation are CPWL. Finally, we prove the existence of minimizers of certain relevant functionals involving the p-Hessian–Schatten total variation in the critical dimension $$d=2$$
d
=
2
.
Funder
Ministero dell’ Istruzione, dell Università e della Ricerca
Scuola Normale Superiore
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mathematics (miscellaneous),Analysis
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1. Linear inverse problems with Hessian–Schatten total variation;Calculus of Variations and Partial Differential Equations;2023-11-20