This work is intended as an introduction to the regularity theory of oriented boundaries in $\Re^n$ 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 hawe some knowledge of the basic facts concerning Caccioppoli sets: sections 2.1 to 2.4 of the book of Massari and Miranda (see [27] of the bibliography at the end of the volume) will serve the scope.
With the exception of a few "classical" inequalities, which proofs can also be found in [27], the exposition is essentially self-contained.
Table Of Contents
| Almost minimal boundaries. |
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1-28 |
| The area excess and de Giorgi's Lemma. |
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29-47 |
| Some preliminary results and the Main Lemma |
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48-75 |
| Proof of the regularity theorem |
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76-87 |
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