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In general, the system of $2$nd-order partial differential equations made ofthe Euler-Lagrange equations of classical field theories are not compatible forsingular Lagrangians. This is the so-called second-order problem. The first aimof this work is to develop a fully geometric constraint algorithm which allowsus to find a submanifold where the Euler-Lagrange equations have solution, andsplit the constraints into two kinds depending on their origin. We do so using$k$-symplectic geometry, which is the simplest intrinsic description ofclassical field theories. As a second aim, the Einstein-Palatini model ofGeneral Relativity is studied using this algorithm.

The second-order problem for $k$-presymplectic Lagrangian field theories. Application to the Einstein--Palatini model