Tobias König

activity

20172026

most citedOn the sharp constant in the Bianchi-Egnell stability inequality

28 citations · 68 across the 14 of their papers we have counts for

collaborators

Showing 2019Show all

3 papers · 1 filter

math.AP2019

Energy asymptotics in the Brezis-Nirenberg problem. The higher-dimensional case

Rupert Frank, Tobias König, Hynek Kovarik

For dimensions $N \geq 4$ , we consider the Brézis-Nirenberg variational problem of finding \[ S(εV) := \inf_{0\not\equiv u\in H^1_0(Ω)} \frac{\int_Ω|\nabla u|^2 \, dx +ε\int_ΩV\, |…

math.AP2019

Energy asymptotics in the three-dimensional Brezis--Nirenberg problem

Rupert L. Frank, Tobias König, Hynek Kovarik

For a bounded open set $Ω \subset R^{3}$ we consider the minimization problem $$ S(a+εV) = \inf_{0\not\equiv u\in H^1_0(Ω)} \frac{\int_Ω(|\nabla u|^2+ (a+εV) |u|^2)\,dx}{(\int_…

math.AP2019

Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity

Rupert L. Frank, Tobias König

We consider positive solutions $u$ of the semilinear biharmonic equation $Δ^{2} u = ∣ x ∣^{- \frac{n + 4}{2}} g (∣ x ∣^{\frac{n - 4}{2}} u)$ in $R^{n} ∖ {0}$ with non-removable s…