In this note, we present some recent regularity results for sets which minimize a weighted notion of perimeter under a weighted volume constraint. We focus on the case of two different densities which are merely α-Hölder continuous, and describe what are the main issues and techniques used in order to establish the optimal regularity C1, α/2-α for the reduced boundary of such sets.
REGULARITY RESULTS FOR ISOPERIMETRIC SETS WITH DENSITY / Cinti E.. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - ELETTRONICO. - 14:2(2023), pp. 22-41. [10.6092/issn.2240-2829/18847]
REGULARITY RESULTS FOR ISOPERIMETRIC SETS WITH DENSITY
Cinti E.
2023
Abstract
In this note, we present some recent regularity results for sets which minimize a weighted notion of perimeter under a weighted volume constraint. We focus on the case of two different densities which are merely α-Hölder continuous, and describe what are the main issues and techniques used in order to establish the optimal regularity C1, α/2-α for the reduced boundary of such sets.File in questo prodotto:
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