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

Showing 2017Show all

5 papers · 1 filter

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…

math.AP2017★ 1 cited

On the strong maximum principle for nonlocal operators

Sven Jarohs, Tobias Weth

In this paper we derive a strong maximum principle for weak supersolutions of nonlocal equations of the form $I u = c (x) u$ in $Ω$ , where $Ω \subset R^{N}$ is a domain, $c\in L^…

math.AP2017★ 2 cited

Starshape of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings

Sven Jarohs, Tadeusz Kulczycki, Paolo Salani

In the present work we study solutions of the problem $- (- Δ)^{α /2} u = f (x, u)$ in $D_{0} ∖ D_{1}$ , with exterior conditions $u = 0$ in $R^{N} ∖ D_{0}$ and $u = 1$ …