arXiv subjects

Gianluigi Manzo

Publications and source records attributed to Gianluigi Manzo.

4 recordsLinked to original sources

arXiv2025

Gradient regularity for double-phase orthotropic functionals

We prove higher integrability for local minimizers of the double-phase orthotropic functional \[ \sum_{i=1}^{n}\int_Ω\left(\left|u_{x_i}\right|^p+a(x)\left| u_{x_i}\right|^q\right)dx \] when the weight function $a \geq0$ is assumed to be $α$-Hölder continuous, while the exponents $p, q$ are such that $2 \leq p \leq q$ and $\frac{q}{p} < 1 + \fracα{n}$. Under natural Sobolev regularity of~$a$, we further obtain explicit Lipschitz regularity estimates for local minimizers.

math.AP↗

arXiv2020

Preduals and double preduals of some Banach spaces

In this paper we study ways to establish when a Banach space can be identified as the dual or the double dual of another Banach space. To obtain these results, we relate these spaces with other, concrete Banach spaces - tipically $\ell^1$ and $\ell^\infty$ - and show that under suitable assumptions we can transfer properties of these spaces to the space we consider. In particular, we show how these results can be used to obtain in a simple way interesting results about spaces such as $BMO$ and $BV$.

math.FA↗

arXiv2020

Atomic decomposition of finite signed measures on compacts of $\mathbb{R}^n$

Recently there has been interest in pairs of Banach spaces $(E_0,E)$ in an $o-O$ relation and with $E_0^{**}=E$. It is known that this can be done for Lipschitz spaces on suitable metric spaces. In this paper we consider the case of a compact subset $K$ of $\mathbb{R}^n$ with the euclidean metric, which does not give an $o-O$ structure, but we use part of the theory concerning these pairs to find an atomic decomposition of the predual of $Lip(K)$. In particular, since the space $\mathfrak{M}(K)$ of finite signed measures on $K$, when endowed with the Kantorovich-Rubinstein norm, has as dual space $Lip(K)$, we can give an atomic decomposition for this space.

math.FA↗

arXiv2019

Duality and distance formulas in Lipschitz-Hölder spaces

For a compact metric space $(K, ρ)$, the predual of $Lip(K, ρ)$ can be identified with the normed space $M(K)$ of finite (signed) Borel measures on $K$ equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of $M(K)$ by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between $Lip(K, ρ)$ and $(lip(K, ρ))_{**}$ [15]. In this work we also show that the pair $(lip(K, ρ), Lip(K, ρ))$ can be framed in the theory of o-O type structures introduced by K. M. Perfekt.

math.FA↗