Rainer Mandel

activity

20112023

most citedOscillating solutions for nonlinear Helmholtz Equations

40 citations · 141 across the 27 of their papers we have counts for

collaborators

36 papers

math.AP2023

Block-radial symmetry breaking for ground states of biharmonic NLS

Rainer Mandel, Diogo Oliveira e Silva

We prove that the biharmonic NLS equation $Δ^{2} u + 2Δ u + (1 + ε) u = ∣ u ∣^{p - 2} u$ in $R^{d}$ has at least $k + 1$ different solutions if $ε > 0$ is small enough and $2…

math.FA2023★ 1 cited

Real Interpolation for mixed Lorentz spaces and Minkowski's inequality

Rainer Mandel

We prove embeddings and identities for real interpolation spaces between mixed Lorentz spaces. This partly relies on Minkowski's (reverse) integral inequality in Lorentz spaces $L^…

math.AP2023

The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs

Rainer Mandel

We prove $L^{p}$ - $L^{q}$ -estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results…

math.AP2022★ 1 cited

Inverse medium scattering for a nonlinear Helmholtz equation

Roland Griesmaier, Marvin Knöller, Rainer Mandel

We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear…

math.AP2022

On Gagliardo-Nirenberg Inequalities with vanishing symbols

Rainer Mandel

We prove interpolation inequalities of Gagliardo-Nirenberg type involving Fourier symbols that vanish on hypersurfaces in $R^{d}$ .

math.AP2021

Ground states for Maxwell's equations in nonlocal nonlinear media

Rainer Mandel

In this paper we investigate the existence of ground states and dual ground states for Maxwell's Equations in $R^{3}$ in nonlocal nonlinear metamaterials. We prove that seve…