Giovanni Cupini

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math.AP2024

A representation formula for regular functions on the characteristic plane of the second Heisenberg group

Annalisa Baldi, Giovanna Citti, Giovanni Cupini

The aim of this paper is to study a Laplace-type operator and its fundamental solution on the characteristic plane in the Heisenberg group $H^{2}$ . We introduce a conformal…

math.AP2023

The Leray-Lions existence theorem under general growth conditions

Giovanni Cupini, Paolo Marcellini, Elvira Mascolo

We prove an existence result of weak solutions $u \in W_{0}^{1, p} (Ω) \cap W_{loc}^{1, q} (Ω)$ , to a Dirichlet problem for a second order elliptic equ…

math.AP2023

Regularity for nonuniformly elliptic equations with $p, q -$ growth and explicit $x, u -$ dependence

Giovanni Cupini, Paolo Marcellini, Elvira Mascolo

We are interested in the regularity of weak solutions $u$ to the elliptic equation in divergence form; precisely in their local boundedness and their local Lipschitz continuity und…

math.AP2023

On the harmonic characterization of the spheres: a sharp stability inequality and some of its consequences

Giovanni Cupini, Ermanno Lanconelli

Let $D$ be a bounded open subset of $R^{n}$ with $∣ \partial D ∣ < \infty$ and let $x_{0}$ be a point of $D$ . We introduce a new parameter, that we call Kuran gap of $\partial…

A representation formula for regular functions on the characteristic plane of the second Heisenberg group

The Leray-Lions existence theorem under general growth conditions

Regularity for nonuniformly elliptic equations with p,q−growth and explicit x,u−dependence

On the harmonic characterization of the spheres: a sharp stability inequality and some of its consequences

Regularity for nonuniformly elliptic equations with $p, q -$ growth and explicit $x, u -$ dependence