# An existence theorem for a non-regular variational problem

@article{Sibner1983AnET, title={An existence theorem for a non-regular variational problem}, author={Lesley Sibner}, journal={manuscripta mathematica}, year={1983}, volume={43}, pages={45-72} }

A “Hodge” theorem is proved for a non-linear system of equations which are not uniformly elliptic. The solutions are p-forms which minimize a non-regular energy functional over cohomology classes. The theorem is proved by regularizing the functional and proving weak L2 existence. To obtain regularity, we first show that a scalar function of the solution is a subsolution of an elliptic equation from which it follows that the solution is bounded. Hölder continuity is then proved by comparison… CONTINUE READING

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## Classical solutions in the Born—Infeld theory

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