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Regularity results for almost minimal oriented hypersurfaces in $$\mathbb R^n$$. (English) Zbl 1191.35007
Quaderni del Dipartimento Matematica dell’Universita de Lecce 1984,1. Lecce: Dipartimento di Matematica dell’Università di Lecce. iii, 92 p. (1984).
This work is intended as an introduction to the regularity theory of oriented boundaries in $$\mathbb R^n$$ which are almost minimal for the area functional. It is based partly on an earlier manuscript which contained the proof of the main theorem presented below, and partly on lecture notes for a course by the author at the University of Lecce.
The reader is presumed to have some knowledge of the basic facts concerning Caccioppoli sets: sections 2.1 to 2.4 of the book of U. Massari and M. Miranda [Minimal surfaces of codimension one. Amsterdam etc.: North-Holland (1984; Zbl 0565.49030)] will serve the scope. With the exception of a few “classical” inequalities, the proofs of which can also be found in the cited book, the exposition is essentially self-contained.

##### MSC:
 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control 35J65 Nonlinear boundary value problems for linear elliptic equations 49Q05 Minimal surfaces and optimization 35A15 Variational methods applied to PDEs