Zobrazeno 1 - 10
of 957
pro vyhledávání: '"Abatangelo A"'
This book is intended as a self-contained introduction to selected topics in the fractional world, focusing particularly on aspects that arise in the study of equations driven by the fractional Laplacian. The scope of this work is not intended to be
Externí odkaz:
http://arxiv.org/abs/2411.18238
Autor:
Abatangelo, Laura, Felli, Veronica
We study double eigenvalues of Aharonov-Bohm operators with Dirichlet boundary conditions in planar domains containing the origin. We focus on the behavior of double eigenvalues when the potential's circulation is a fixed half-integer number and the
Externí odkaz:
http://arxiv.org/abs/2410.23917
The Grushin Laplacian $- \Delta_\alpha $ is a degenerate elliptic operator in $\mathbb{R}^{h+k}$ that degenerates on $\{0\} \times \mathbb{R}^k$. We consider weak solutions of $- \Delta_\alpha u= Vu$ in an open bounded connected domain $\Omega$ with
Externí odkaz:
http://arxiv.org/abs/2410.12637
Consider the following Lane-Emden system with Dirichlet boundary conditions: \[ -\Delta U = |V|^{\beta-1}V,\ -\Delta V = |U|^{\alpha-1}U \text{ in }\Omega,\qquad U=V= 0 \text{ on }\partial \Omega, \] in a bounded domain $\Omega$, for $(\alpha,\beta)$
Externí odkaz:
http://arxiv.org/abs/2312.16696
Publikováno v:
ESAIM Control Optim. Calc. Var., 30 (2024), Article number: 52, 49 pages
We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the (volume) avera
Externí odkaz:
http://arxiv.org/abs/2308.01569
We provide a full series expansion of a generalization of the so-called $u$-capacity related to the Dirichlet-Laplacian in dimension three and higher, extending previous results of the authors, and of the authors together with Virginie Bonnaillie-No\
Externí odkaz:
http://arxiv.org/abs/2305.06953
Autor:
Abatangelo, Laura, Ognibene, Roberto
We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of the pertur
Externí odkaz:
http://arxiv.org/abs/2301.11729
Autor:
Abatangelo, Nicola, Jarohs, Sven
We collect some peculiarities of higher-order fractional Laplacians $(-\Delta)^s$, $s>1$, with special attention to the range $s\in(1,2)$, which show their oscillatory nature. These include the failure of the polarization and P\'olya-Szeg\"o inequali
Externí odkaz:
http://arxiv.org/abs/2205.12610
Autor:
Abatangelo, Nicola, Jarohs, Sven
We show that the first eigenfunction of the fractional Laplacian ${(-\Delta)}^s$, $s\in(1/2,1)$, is superharmonic in the unitary ball up to dimension $11$. To this aim, we also rely on a computer-assisted step to estimate a rather complicated constan
Externí odkaz:
http://arxiv.org/abs/2204.14149
We provide a Hopf boundary lemma for the regional fractional Laplacian $(-\Delta)^s_{\Omega}$, with $\Omega\subset\mathbb{R}^N$ a bounded open set. More precisely, given $u$ a pointwise or weak super-solution of the equation $(-\Delta)^s_{\Omega} u =
Externí odkaz:
http://arxiv.org/abs/2112.09522