On the existence of discontinuous solutions for a class of multidimensional quasiregular variational problems

In this paper the existence of discontinuous solutions $x^{n+1}=u(x)$, $x\in\Omega$, of a positive definite quasiregular $n$-dimensional variational problem is established when the order of growth of the integrand of the functional degenerates up to unity on non-self-intersecting $(n-1)$-dimensional surfaces lying in the region $\Omega$ or on its boundary $S$.
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