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Some optimal control and shape optimisation problems for bulk-surface cooperative systems
Andrea Gentile, Idriss Mazari-Fouquer, Raphaël Prunier
The goal of this paper is to address some optimal control and shape optimisation problems arising from bulk-surface cooperative systems. The basic model under consideration is the…
Isoperimetric estimates for solutions to the p-Laplacian with variable Robin boundary conditions
Vincenzo Amato, Francesco Chiacchio, Andrea Gentile
In this paper we study the -Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we pr…
Higher differentiability results for solutions to a class of non-homogeneouns elliptic problems under sub-quadratic growth conditions
Albert Clop, Andrea Gentile, Antonia Passarelli di Napoli
We prove a sharp higher differentiability result for local minimizers of functionals of the form $$\mathcal{F}\left(w,Ω\right)=\int_Ω\left[ F\left(x,Dw(x)\right)-f(x)\cdot w(x)\rig…
Regularity results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions
Andrea Gentile, Raffaella Giova
We establish some higher differentiability results for solution to non-autonomous obstacle problems of the form \begin{equation*} \min \left\{\int_Ωf\left(x, Dv(x)\right)dx\,:\, v\…
Regularity results for bounded solutions to obstacle problems with non-standard growth conditions
Andrea Gentile, Raffaella Giova, Andrea Torricelli
In this paper we consider a class of obstacle problems of the type %\begin{equation*} %\int_Ω\left<A(x, Du), D(φ-u)\right> \, \dx\ge0\qquad\forall %φ\in W^{1,q}(Ω) \quad {\mathrm{s…
Comparison results for solutions to p-Laplace equations with Robin boundary conditions
Vincenzo Amato, Andrea Gentile, Alba Lia Masiello
In the last decades comparison results of Talenti type for Elliptic Problems with Dirichlet boundary conditions have been widely investigated. In this paper, we generalize the resu…