Author:
Beck Lisa,Cinti Eleonora,Seis Christian
Abstract
AbstractWe establish a regularity result for optimal sets of the isoperimetric problem with double density under mild ($$\alpha $$
α
-)Hölder regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to reach in any dimension the regularity class $$C^{1,\frac{\alpha }{2-\alpha }}$$
C
1
,
α
2
-
α
. This class is indeed the optimal one for local minimizers of variational functionals with an integrand that depends $$\alpha $$
α
-Hölder continuous on the minimizer itself, and as such can (the boundary of) the isoperimetric set be locally written (with additional constraint).
Funder
Alma Mater Studiorum - Università di Bologna
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference16 articles.
1. Ambrosio, L., Carlotto, A., Massaccesi, A.: Lectures on Elliptic Partial Differential Equations. Edizioni della Normale, Pisa (2018)
2. Beck, L.: Elliptic regularity theory. A first course. Lecture Notes of the Unione Matematica Italiana, 19. Springer, Cham; Unione Matematica Italiana, Bologna (2016). xii+201 pp
3. Campanato, S.: Proprietà di Hölderianità di alcune classi di funzioni. Ann. Sc. Norm. Super. Pisa Ser. III(17), 175–188 (1963)
4. Cinti, E., Pratelli, A.: $$\varepsilon -\varepsilon ^\beta $$property, boundedness of isoperimetric sets and applications. J. Reine Angew. Math. 728, 65–103 (2017)
5. Cinti, E., Pratelli, A.: Regularity of isoperimetric sets with density in dimension 2. Math. Ann. 368(1–2), 419–432 (2017)
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