Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Jarohs, Sven"'
We introduce and study the logarithmic $p$-Laplacian $L_{\Delta_p}$, which emerges from the formal derivative of the fractional $p$-Laplacian $(-\Delta_p)^s$ at $s=0$. This operator is nonlocal, has logarithmic order, and is the nonlinear version of
Externí odkaz:
http://arxiv.org/abs/2411.11181
In this work, we study the asymptotic behavior of the free boundary of the solution to the exterior Bernoulli problem for the half Laplacian when the Bernoulli's gradient parameter tends to $0^+$ and to $+\infty$. Moreover, we show that, under suitab
Externí odkaz:
http://arxiv.org/abs/2409.17810
Let $u_s$ denote a solution of the fractional Poisson problem $$ (-\Delta)^s u_s = f\quad\text{ in }\Omega,\qquad u_s=0\quad \text{ on }\mathbb{R}^N\setminus \Omega, $$ where $N\geq 2$ and $\Omega\subset \mathbb{R}^N$ is a bounded domain of class $C^
Externí odkaz:
http://arxiv.org/abs/2311.18476
We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional Laplacian as the
Externí odkaz:
http://arxiv.org/abs/2311.13079
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
Autor:
Djitte, Sidy M., Jarohs, Sven
In the present paper, we study properties of the second Dirichlet eigenvalue of the fractional Laplacian of annuli-like domains and the corresponding eigenfunctions. In the first part, we consider an annulus with inner radius $R$ and outer radius $R+
Externí odkaz:
http://arxiv.org/abs/2201.04907
Autor:
Feulefack, Pierre Aime, Jarohs, Sven
In this work we study nonlocal operators and corresponding spaces of order strictly below one and investigate interior regularity properties of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side. Our m
Externí odkaz:
http://arxiv.org/abs/2112.09364
We study the exterior and interior Bernoulli problems for the half Laplacian and the interior Bernoulli problem for the spectral half Laplacian. We concentrate on the existence and geometric properties of solutions. Our main results are the following
Externí odkaz:
http://arxiv.org/abs/2112.05479
Autor:
Djitte, Sidy M., Jarohs, Sven
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has a fixed s
Externí odkaz:
http://arxiv.org/abs/2109.14024