Geodesic
Liouville-type results in two dimensions for stationary points of functionals with linear growth
Michael Bildhauer1 ; Martin Fuchs1
1Saarland University, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 417-426

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We consider elliptic systems generated by variational integrals of linear growth satisfying the condition of $\mu$-ellipticity for some exponent $\mu >1$ and prove that stationary points $u\colon\mathbb{R}^2\to\mathbb{R}^N$ with the property $\limsup_{|x|\to \infty} \frac{|u(x)|}{|x|} < \infty$ must be affine functions. The latter condition can be dropped in the scalar case together with appropriate assumptions on the energy density providing an extension of Bernstein's theorem.
DOI : 10.54330/afm.114681
Keywords: Variational problems, linear growth, entire solutions in 2D, Liouville and Bernstein-type results

Michael Bildhauer  1   ; Martin Fuchs  1

1 Saarland University, Department of Mathematics 
Michael Bildhauer; Martin Fuchs. Liouville-type results in two dimensions for stationary points of functionals with linear growth. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 417-426. doi: 10.54330/afm.114681
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