Calculus of Variations and Geometric Measure Theory
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I. Tamanini

Regularity results for almost minimal oriented hypersurfaces in $\mathbb R^N$

created by root on 16 Mar 2012

[BibTeX]

Lecture Notes

Inserted: 16 mar 2012
Last Updated: 16 mar 2012

Journal: Quaderni del Dipartimento di Matematica dell'Università del Salento
Volume: 1
Pages: 1-92
Year: 1984
Links: journal site (full PDF available)

Abstract:

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 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.

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