Simone Creo

Sapienza University of Rome | la sapienza · Department of Basic and Applied Sciences for Engineering

We consider a parabolic semilinear non-autonomous problem $(\tilde P)$ for a fractional time-dependent operator $\mathcal{B}^{s,t}_\Omega$ with Venttsel'-type boundary conditions in an extension domain $\Omega\subset\mathbb{R}^N$ having as boundary a $d$-set. We prove existence and uniqueness of the mild solution of the associated semilinear abstra...

We consider a parabolic transmission problem, involving nonlinear fractional operators of different order, across a fractal interface \begin{document}$ \Sigma $\end{document}. The transmission condition is of Robin type and it involves the jump of the \begin{document}$ p $\end{document}-fractional normal derivatives on the irregular interface. Afte...

We consider a quasi-linear homogenization problem in a two-dimensional pre-fractal domain $\Omega_n$, for $n\in\mathbb{N}$, surrounded by thick fibers of amplitude $\varepsilon$. We introduce a sequence of "pre-homogenized" energy functionals and we prove that this sequence converges in a suitable sense to a quasi-linear fractal energy functional i...

We study a nonlocal Robin–Venttsel’-type problem for the regional fractional p-Laplacian in an extension domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega...

We study the asymptotic behavior of anomalous p-fractional energies in bad domains via the M-convergence. These energies arise naturally when studying Robin-Venttsel’ problems for the regional fractional p-Laplacian. We provide a suitable notion of fractional normal derivative on irregular sets via a fractional Green formula as well as existence an...

We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori esti...

We consider parabolic nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution.

We study the asymptotic behavior of anomalous fractional diffusion processes in bad domains via the convergence of the associated energy forms. We introduce the associated Robin–Venttsel’ problems for the regional fractional Laplacian. We provide a suitable notion of fractional normal derivative on irregular sets via a fractional Green formula as w...

We prove a generalized version of Friedrichs and Gaffney inequalities for a bounded $(\varepsilon,\delta)$ domain $\Omega\subset\mathbb{R}^n$, $n=2,3$, by adapting the methods of Jones to our framework.

We study a nonlocal Venttsel' problem in a non-convex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out and optimal a priori error estimates are obtained.

We prove a generalized version of Friedrichs and Gaffney inequalities for a bounded $(\varepsilon,\delta)$ domain $\Omega\subset\mathbb{R}^n$, $n=2,3$, by adapting the methods of Jones to our framework.

In this paper we study a quasi-linear evolution equation with nonlinear dynamical boundary conditions in a three dimensional fractal cylindrical domain $Q$, whose lateral boundary is a fractal surface $S$. We consider suitable approximating pre-fractal problems in the corresponding pre-fractal varying domains. After proving existence and uniqueness...

We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal one. We consider the numerical approximation of the pre-fractal problems via FEM and we prove a pr...

We study a quasi-linear evolution equation with nonlinear dynamical boundary conditions in a two dimensional fractal domain. We consider suitable approximating pre-fractal problems in the corresponding pre-fractal varying domains. After proving existence and uniqueness results via standard semigroup approach, we prove that the pre-fractal solutions...

We study a quasi-linear evolution equation with nonlinear dynamical boundary conditions in a two dimensional domain with Koch-type fractal boundary. We consider suitable approximating pre-fractal problems in the corresponding pre-fractal varying domains. After proving existence and uniqueness results via standard semigroup approach, we prove that t...

We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains.