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We study solutions of Euler–Lagrange equations for isotropic energy functionals, generalizing a previous result on  p -harmonic mappings. We classify all stored energy functions which give rise to a first-order differential expression whose Laplacian involves no third derivatives of the stationary solution. This classification gives rise to a new technique of finding subharmonicity results for the variational equations, and we also illustrate this technique in two examples. Firstly, we prove a subharmonicity result for the Jacobian determinant in the case of weighted Dirichlet energy. Secondly, we find optimal subharmonicity results in the case of a Neohookean-type stored energy function.

Subharmonicity results for the stationary solutions of isotropic energy functionals