Some Isoperimetric Problems in Planes with Density
By Antonio Cañete, Michele Miranda Jr., Davide Vittone. 2009
66 citations recorded by the source corpus.
We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also consider continuous modification of Gauss density in ℝ2. Finally, we give a list of related open questions.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9afa22e15c14b46b79ee204099b3d420a7c467dd
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In Applied Mathematics
- Andrea Cianchi
- Lenka Slav'ikov'a
- L. Pick
- Aldo Pratelli
- Emanuel Milman
- Alessio Figalli
- Iwona Chlebicka
- N. Fusco
In Mathematical Physics
- Lenka Slav'ikov'a
- L. Pick
- Andrea Cianchi
- Aldo Pratelli
- Iwona Chlebicka
- Emanuel Milman
- Alessio Figalli
- P. Hasto
Citations in the corpus
- Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “ic inequalities is very rich. Let us limit ourselves to mentioning that, besides those quoted above, recent contributions on isoperimetric problems in (domains in) Rn endowed with a measure ν include [18, 36, 43, 76]. Given a Banach function space X(Ω,ν) of measurable functions on Ω, and a positive ”
- Existence of isoperimetric regions in R n with density (2011, background): “in are stable, while if vis strictly concave, then balls are unstable. More precisely, the second variation of perimeter for xed volume for the ball B(r) has the same sign as v"(r). Example 2.5 ([3], Theorems 3.23, 3.20). Consider R2 with density 0 <<1 inside the unit ball and density 1 o”