Marco Capolli
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View article: Morrey–Campanato functional spaces for Carnot groups
Morrey–Campanato functional spaces for Carnot groups Open
We shortly review the historical path of Morrey–Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey–Campanato spaces in…
View article: Harmonic Curves From Euclidean Domains to Heisenberg Group H1
Harmonic Curves From Euclidean Domains to Heisenberg Group H1 Open
We define and study the harmonic curves on domains in $\mathbb{R}^n$ into the first Heisenberg group $\mathbb{H}^1$. These are the $C^2$-regular mappings which are critical points of the second Dirichlet energy and satisfy the weak isotrop…
View article: Morrey-Campanato Functional Spaces for Carnot Groups
Morrey-Campanato Functional Spaces for Carnot Groups Open
We shortly review the historical path of Morrey-Campanato functional spaces and the fundamentals of Carnot groups. Then, we merge these two topics, by recovering several classical results concerning regularity of Morrey-Campanato spaces in…
View article: A survey on Lyapunov functions for epidemic compartmental models
A survey on Lyapunov functions for epidemic compartmental models Open
In this survey, we propose an overview on Lyapunov functions for a variety of compartmental models in epidemiology. We exhibit the most widely employed functions, together with a commentary on their use. Our aim is to provide a comprehensi…
View article: An Overview on Laakso Spaces
An Overview on Laakso Spaces Open
Laakso's construction is a famous example of an Ahlfors $Q$-regular metric measure space admitting a weak $(1,1)$-Poincaré inequality that can not be embedded in $\mathbb{R}^n$ for any $n$. The construction is of particular interest becaus…
View article: Maximal Directional Derivatives in Laakso Space
Maximal Directional Derivatives in Laakso Space Open
We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiabi…
View article: A Generalization of Lanchester's Model of Warfare
A Generalization of Lanchester's Model of Warfare Open
The classical Lanchester's model is shortly reviewed and analysed, with particular attention to the critical issues that intrinsically arise from the mathematical formalization of the problem. We then generalize a particular version of suc…
View article: A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups
A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups Open
We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We prove that k-approximate differentiability almost everywhere is equivalent to admitting a Lusin approximation by $C^{k}_{\mathbb{G}}$ maps. …
View article: On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot groups
On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot groups Open
In this note we study the limit as $s\downarrow 0$ of fractional Orlicz-Sobolev seminorms in Carnot groups. This closes the study started in [10]
View article: On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot\n groups
On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot\n groups Open
In this note we study the limit as $s\\downarrow 0$ of fractional\nOrlicz-Sobolev seminorms in Carnot groups. This closes the study started in\n[10]\n