5 papers
Classification of solutions of an equation related to a conformal log Sobolev inequality
Rupert L. Frank, Tobias König, Hanli Tang
We classify all finite energy solutions of an equation which arises as the Euler--Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to B…
Energy asymptotics in the Brezis-Nirenberg problem. The higher-dimensional case
Rupert Frank, Tobias König, Hynek Kovarik
For dimensions , 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\, |…
Energy asymptotics in the three-dimensional Brezis--Nirenberg problem
Rupert L. Frank, Tobias König, Hynek Kovarik
For a bounded open set 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_…
Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity
Rupert L. Frank, Tobias König
We consider positive solutions of the semilinear biharmonic equation in with non-removable s…
Liquid Drop Model for Nuclear Matter in the Dilute Limit
Lukas Emmert, Rupert L. Frank, Tobias König
We consider the liquid drop model for nuclei interacting with a neutralizing homogeneous background of electrons. The regime we are interested in is when the fraction between the e…