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Recently it has been shown that the unique local perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens, hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem.
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The isoperimetric problem in the plane with the sum of two Gaussian densities
We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the plane are half-spaces, then they must be bounded by vertical lines.
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- PAR ID:
- 10054850
- Date Published:
- Journal Name:
- Involve
- Volume:
- 11
- Issue:
- 4
- ISSN:
- 1944-4184
- Page Range / eLocation ID:
- 549-567
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.2140/involve.2018.11.549
