Zobrazeno 1 - 10
of 165
pro vyhledávání: '"Kogoj, A. E."'
Autor:
Kogoj, Alessia E., Lanconelli, E.
Let $D\subseteq \mathbb{R}^n$, $n\geq 3$, be a bounded open set and let $x_0\in D$. Assume that the Newtonian potential of $D$ is proportional outside $D$ to the Newtonian potential of a mass concentrated at $\{x_0\}.$ Then $D$ is a Euclidean ball ce
Externí odkaz:
http://arxiv.org/abs/2411.00961
Autor:
Kogoj, Alessia E., Lanconelli, Ermanno
By exploiting an old idea first used by Pizzetti for the classical Laplacian, we introduce a notion of {\it asymptotic average solutions} making pointwise solvable every Poisson equation $\mathcal{L} u(x)=-f(x)$ with continuous data $f$, where $\math
Externí odkaz:
http://arxiv.org/abs/2209.08394
Autor:
Goldstein, Gisele R., Goldstein, Jerome A., Kogoj, Alessia E., Rhandi, Abdelaziz, Tacelli, Cristian
In this paper we generalize the instantaneous blowup result from [3] and [15] to the heat equation perturbed by singular potentials on the Heisenberg group.
Externí odkaz:
http://arxiv.org/abs/2204.04548
Autor:
Kogoj, Alessia E., Lanconelli, Ermanno
By an easy trick taken from caloric polynomial theory we construct a family $\mathscr{B}$ of $almost\ regular$ domains for the caloric Dirichlet problem. $\mathscr{B}$ is a basis of the Euclidean topology. This allows to build, with a basically eleme
Externí odkaz:
http://arxiv.org/abs/2106.10475
We prove, with a purely analytic technique, a one-side Liouville theorem for a class of Ornstein--Uhlenbeck operators ${\mathcal L_0}$ in $\mathbb{R}^N$, as a consequence of a Liouville theorem at "$t=- \infty$" for the corresponding Kolmogorov opera
Externí odkaz:
http://arxiv.org/abs/2002.04718
Autor:
Kogoj, Alessia E.
We consider the linear second order PDO's $$ \mathscr{L} = \mathscr{L}_0 - \partial_t : = \sum_{i,j =1}^N \partial_{x_i}(a_{i,j} \partial_{x_j} ) - \sum_{j=i}^N b_j \partial_{x_j} - \partial _t,$$and assume that $\mathscr{L}_0$ has nonnegative charac
Externí odkaz:
http://arxiv.org/abs/1903.08463
We establish a necessary and sufficient condition for a boundary point to be regular for the Dirichlet problem related to a class of Kolmogorov-type equations. Our criterion is inspired by two classical criteria for the heat equation: the Evans-Garie
Externí odkaz:
http://arxiv.org/abs/1701.01073
Autor:
Kogoj, Alessia E.
We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient
Externí odkaz:
http://arxiv.org/abs/1606.07133
Autor:
Kogoj, Alessia E., Polidoro, Sergio
We consider nonnegative solutions $u:\Omega\longrightarrow \mathbb{R}$ of second order hypoelliptic equations \begin{equation*} \mathscr{L} u(x) =\sum_{i,j=1}^n \partial_{x_i} \left(a_{ij}(x)\partial_{x_j} u(x) \right) + \sum_{i=1}^n b_i(x) \partial_
Externí odkaz:
http://arxiv.org/abs/1509.05245
Autor:
Bonfiglioli, Andrea, Kogoj, Alessia E.
We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space. We show that a natural weight is the right
Externí odkaz:
http://arxiv.org/abs/1503.01801