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math.AP2021
Small weights in Caccioppoli's inequality and applications to Liouville-type theorems for non-standard problems
Michael Bildhauer, Martin Fuchs
Using a variant of Caccioppoli's inequality involving small weights, i.e. weights of the form for some , we establish several Liouville-type theorem…
math.AP2021
An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler-Lagrange equations related to general linear growth problems
Michael Bildhauer, Martin Fuchs
A famous theorem of Bers and Finn states that isolated singularities of solutions to the non-parametric minimal surface equation are removable. We show that this result remains val…
math.AP2021
Liouville-type results in two dimensions for stationary points of functionals with linear growth
Michael Bildhauer, Martin Fuchs
We consider variational integrals of linear growth satisfying the condition of -ellipticity for some exponent and prove that stationary points : $\mathbb{R}^2 \to \math…