Zobrazeno 1 - 10
of 210
pro vyhledávání: '"Ferrari, Fausto"'
Autor:
Ferrari, Fausto, Merlino, Enzo Maria
In this paper, in a Carnot group $\mathbb{G}$ of step $2$ and homogeneous dimension $Q$, we prove that almost minimizers of the (horizontal) one-phase $p$-Bernoulli-type functional $$ J_p(u,\Omega):=\int_{\Omega}\Big( |\nabla_{\mathbb{G}} u(x)|^p+\ch
Externí odkaz:
http://arxiv.org/abs/2407.00084
In this paper, we prove that flat free boundaries of solutions to inhomogeneous one-phase Stefan problem are $C^{1,\alpha}$.
Externí odkaz:
http://arxiv.org/abs/2404.07535
We prove that nonnegative almost minimizers of the horizontal Bernoulli-type functional $$ J(u,\Omega):=\int_{\Omega}\Big(|\nabla_{\mathbb{G}} u(x)|^2+\chi_{\{u>0\}}(x)\Big)\,dx$$ are Lipschitz continuous in the intrinsic sense.
Externí odkaz:
http://arxiv.org/abs/2311.02975
Autor:
Corni, Francesca, Ferrari, Fausto
In this paper we construct the fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation approach. In addition, we characterize the powers of the fractional sub-Laplacian in the Heisenberg group, and as a byproduct we c
Externí odkaz:
http://arxiv.org/abs/2310.17387
Autor:
Ferrari, Fausto, Forcillo, Nicolò
Publikováno v:
Boll Unione Mat Ital (2023)
In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we sho
Externí odkaz:
http://arxiv.org/abs/2310.13264
Autor:
Ferrari, Fausto, Lederman, Claudia
We continue our study in \cite{FL} on viscosity solutions to a one-phase free boundary problem for the $p(x)$-Laplacian with non-zero right hand side. We first prove that viscosity solutions are locally Lipschitz continuous, which is the optimal regu
Externí odkaz:
http://arxiv.org/abs/2305.07418
We prove that, given~$p>\max\left\{\frac{2n}{n+2},1\right\}$, the nonnegative almost minimizers of the nonlinear free boundary functional $$ J_p(u,\Omega):=\int_{\Omega}\Big( |\nabla u(x)|^p+\chi_{\{u>0\}}(x)\Big)\,dx$$ are Lipschitz continuous.
Externí odkaz:
http://arxiv.org/abs/2206.03238
In this paper we give an overview of some recent and older results concerning free boundary problems governed by elliptic operators.
Externí odkaz:
http://arxiv.org/abs/2204.04942
Autor:
Ferrari, Fausto, Forcillo, Nicolò
Publikováno v:
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 34 (2023)
In this paper we provide a counterexample about the existence of an increasing monotonicity behavior of a function introduced in \cite{FeFo}, companion of the celebrated Alt-Caffarelli-Friedman monotonicity formula, in the noncommutative framework.
Externí odkaz:
http://arxiv.org/abs/2203.06232
Autor:
Ferrari, Fausto, Manfredi, Juan J.
In this paper we prove a H\"older regularity estimate for viscosity solutions of inhomogeneous equations governed by the infinite Laplace operator relative to a frame of vector fields.
Externí odkaz:
http://arxiv.org/abs/2106.11183