On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot groups
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]
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arXiv subjects
Ariel Martin Salort
Publications and source records attributed to Ariel Martin Salort.
Maz'ya-Shaposhnikova formula in Magnetic Fractional Orlicz-Sobolev spaces
In this note we prove the validity of the Maz'ya-Shaposhnikova formula in magnetic fractional Orlicz-Sobolev spaces. This complements a previous study of the limit as $s \uparrow 1$ performed by the second author in [21].
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Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot groups
In this article we define a class of fractional Orlicz-Sobolev spaces on Carnot groups and, in the spirit of the celebrated results of Bourgain-Brezis-Mironescu and of Maz'ya-Shaposhnikova, we study the asymptotic behavior of the Orlicz functionals when the fractional parameter goes to $1$ and $0$.
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Shape optimization problems for nonlocal operators
In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze the transition from nonlocal to local state equations.
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Asymptotic behavior of the curves in the Fu{č}{\'ı}k spectrum
In this work we study the asymptotic behavior of the curves of the Fu{č}{\'ı}k spectrum for weighted second order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the spectrum in terms of some integrals of the weights. We present an algorithm which computes the intersection of the Fu{č}{\'ı}k spectrum with rays through the origin, and we compare their values with the asymptotic ones.
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Homogenization of Fučík eigencurves
In this work we study the convergence of an homogenization problem for half-eigenvalues and Fučík eigencurves. We provide quantitative bounds on the rate of convergence of the curves for periodic homogenization problems.
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