Sven Jarohs

activity

20132026

most citedOn the maximum principle for higher-order fractional Laplacians

27 citations · 60 across the 24 of their papers we have counts for

collaborators

31 papers

math.AP2026

$s$ -harmonic functions in the small order limit

Sven Jarohs, Abhrojyoti Sen, Tobias Weth

We study families $u_{s}$ of functions satisfying the equations $(- Δ)^{s} u_{s} = 0$ , $s \in (0, 1)$ in a smooth bounded open set $Ω \subset R^{N}$ . The main purpose of this paper is…

math.AP2025

On a class of (non)local superposition operators of arbitrary order

Serena Dipierro, Sven Jarohs, Enrico Valdinoci

In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples…

math.AP2024

The Dirichlet Problem For the Logarithmic p-Laplacian

Bartłomiej Dyda, Sven Jarohs, Firoj Sk

We introduce and study the logarithmic $p$ -Laplacian $L_{Δ_{p}}$ , which emerges from the formal derivative of the fractional $p$ -Laplacian $(- Δ_{p})^{s}$ at $s = 0$ . This operator is nonlo…

math.AP2024

Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian

Sven Jarohs, Tadeusz Kulczycki, Paolo Salani

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…

math.AP2023

Differentiability of the nonlocal-to-local transition in fractional Poisson problems

Alberto Saldaña, Sven Jarohs, Tobias Weth

Let $u_{s}$ denote a solution of the fractional Poisson problem $(- Δ)^{s} u_{s} = f in Ω, u_{s} = 0 on R^{N} ∖ Ω,$ where $N \geq 2$ and $Ω\sub…

math.AP2023

Continuity of solutions to equations with weakly singular nonlocal operators

Sven Jarohs, Moritz Kassmann, Tobias Weth

We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differenti…

math.NA2023

FEM for 1D-problems involving the logarithmic Laplacian: error estimates and numerical implementation

Víctor Hernández-Santamaría, Sven Jarohs, Alberto Saldaña +1

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…

math.AP2022

Oscillatory Phenomena for Higher-Order Fractional Laplacians

Nicola Abatangelo, Sven Jarohs

We collect some peculiarities of higher-order fractional Laplacians $(- Δ)^{s}$ , $s > 1$ , with special attention to the range $s \in (1, 2)$ , which show their oscillatory nature. These inc…

math.AP2022

On the shape of the first fractional eigenfunction

Nicola Abatangelo, Sven Jarohs

We show that the first eigenfunction of the fractional Laplacian $(- Δ)^{s}$ , $s \in (1/2, 1)$ , is superharmonic in the unitary ball up to dimension $11$ . To this aim, we also rely on…

math.AP2022★ 1 cited

Nonradiality of second fractional eigenfunctions of thin annuli

Sidy M. Djitte, Sven Jarohs

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 p…

math.AP2021

On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian

Sven Jarohs, Tadeusz Kulczycki, Paolo Salani

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…

math.AP2021

Nonlocal operators of small order

Pierre Aime Feulefack, Sven Jarohs

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 Poi…

math.AP2021

Symmetry of odd solutions to equations with fractional Laplacian

Sidy M. Djitte, Sven Jarohs

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 co…

math.AP2020★ 1 cited

Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian

Pierre Aime Feulefack, Sven Jarohs, Tobias Weth

In this article, we study the asymptotics of Dirichlet eigenvalues and eigenfunctions of the fractional Laplacian $(- Δ)^{s}$ in bounded open Lipschitz sets in the small order limit $…

math.AP2020

Fractional Laplacians on ellipsoids

Nicola Abatangelo, Sven Jarohs, Alberto Saldaña

We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians of some functions supported on ellipsoids. In particular, we derive the explicit expre…

math.AP2019

Foliated Schwarz symmetry of solutions to a cooperative system of equations involving nonlocal operators

Antonio Greco, Sven Jarohs

In this paper, we prove foliated Schwarz symmetry of solutions to a cooperatively coupled system of equations involving nonlocal operators. Here, the class of nonlocal operators co…

math.AP2019

A new look at the fractional Poisson problem via the Logarithmic Laplacian

Sven Jarohs, Alberto Saldana, Tobias Weth

We analyze the $s$ -dependence of solutions $u_{s}$ to the family of fractional Poisson problems $(- Δ)^{s} u = f$ in $Ω$ , $u \equiv 0$ on $R^{N} ∖ Ω$ in an open bounded set…

math.AP2019

Gradient estimates in fractional Dirichlet problems

Mouhamed Moustapha Fall, Sven Jarohs

We obtain some fine gradient estimates near the boundary for solutions to fractional elliptic problems subject to exterior Dirichlet boundary conditions. Our results provide, in pa…

math.AP2019

On overdetermind problems for a general class of nonlocal operators

Anup Biswas, Sven Jarohs

We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractiona…

math.AP2018

Local compactness and nonvanishing for weakly singular nonlocal quadratic forms

Sven Jarohs, Tobias Weth

In this work we study a class of nonlocal quadratic forms given by \[ \mathcal{E}_j(u,v)=\frac{1}{2}\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}(u(x)-u(y))(v(x)-v(y))j(x-y)\ dxdy, \] whe…

math.AP2018

Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions

Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall +2

We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the ope…

math.AP2017

Positive powers of the Laplacian: from hypersingular integrals to boundary value problems

Nicola Abatangelo, Sven Jarohs, Alberto Saldaña

Any positive power of the Laplacian is related via its Fourier symbol to a hypersingular integral with finite differences. We show how this yields a pointwise evaluation which is m…

math.AP2017★ 21 cited

Integral representation of solutions to higher-order fractional Dirichlet problems on balls

Nicola Abatangelo, Sven Jarohs, Alberto Saldaña

We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power $s > 0$ of the Laplacian. We are able to prescribe values…

math.AP2017

Strong comparison principle for the fractional $p$ -Laplacian and applications to starshaped rings

Sven Jarohs

In the following we show the strong comparison principle for the fractional $p$ -Laplacian, i.e. we analyze functions $v, w$ which satisfy $v \geq w$ in $R^{N}$ and \[ (-Δ)^s_p…

s-harmonic functions in the small order limit

On a class of (non)local superposition operators of arbitrary order

The Dirichlet Problem For the Logarithmic p-Laplacian

Qualitative properties of free boundaries for the exterior Bernoulli problem for the half Laplacian

Differentiability of the nonlocal-to-local transition in fractional Poisson problems

Continuity of solutions to equations with weakly singular nonlocal operators

FEM for 1D-problems involving the logarithmic Laplacian: error estimates and numerical implementation

Oscillatory Phenomena for Higher-Order Fractional Laplacians

On the shape of the first fractional eigenfunction

Nonradiality of second fractional eigenfunctions of thin annuli

On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian

Nonlocal operators of small order

Symmetry of odd solutions to equations with fractional Laplacian

Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian

Fractional Laplacians on ellipsoids

Foliated Schwarz symmetry of solutions to a cooperative system of equations involving nonlocal operators

A new look at the fractional Poisson problem via the Logarithmic Laplacian

Gradient estimates in fractional Dirichlet problems

On overdetermind problems for a general class of nonlocal operators

Local compactness and nonvanishing for weakly singular nonlocal quadratic forms

Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions

Positive powers of the Laplacian: from hypersingular integrals to boundary value problems

Integral representation of solutions to higher-order fractional Dirichlet problems on balls

Strong comparison principle for the fractional p-Laplacian and applications to starshaped rings

$s$ -harmonic functions in the small order limit

Strong comparison principle for the fractional $p$ -Laplacian and applications to starshaped rings