Geodesic
On entire solutions of the equations for the displacement fields in the deformation theory of plasticity with logarithmic hardening
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Tome 397 (2011), pp. 157-171 
M. Fuchs; G. Zhang. On entire solutions of the equations for the displacement fields in the deformation theory of plasticity with logarithmic hardening. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Tome 397 (2011), pp. 157-171. http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a8/
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     title = {On entire solutions of the equations for the displacement fields in the deformation theory of plasticity with logarithmic hardening},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a8/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $u\colon\mathbb R^2\to\mathbb R^2$ denote an entire solution of the homogeneous Euler–Lagrange equation associated to the energy used in the deformation theory of plasticity with logarithmic hardening. If $|u(x)|$ is of slower growth than $|x|$ as $|x|\to\infty$, then $u$ must be constant. Moreover we show that $u$ is affine if either $\sup_{\mathbb R^2}|\nabla u|<\infty$ or $\limsup_{|x|\to\infty}|x|^{-1}|u(x)|<\infty$.

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