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Regularity of solutions to elliptic isoperimetric problems

Regularity of solutions to elliptic isoperimetric problems

In an earlier paper by the author, the existence theory for solutions of elliptic isoperimetric problems was developed in the context of rectifiable and integral currents.The regularity problem for solutions of those isoperimetric problems was essentially left open.Examples were given to show that, in certain cases, regularity may be totally …