Nondegeneracy of standard double bubbles

2019 ◽  
Vol 147 (10) ◽  
pp. 4379-4395
Author(s):  
Gianmichele Di Matteo
Keyword(s):  
Double Bubbles

scholarly journals Symmetric double bubbles in the Grushin plane

2019 ◽  
Vol 25 ◽  
pp. 77
Author(s):  
Valentina Franceschi ◽  
Giorgio Stefani
Keyword(s):  
Direct Method ◽  
Regularity Theory ◽  
Contact Interface ◽  
Double Bubble ◽  
Grushin Plane ◽  
Existence Of Minimizers ◽  
Double Bubbles ◽  
The Given ◽  
Suitable Change ◽  
Horizontal Interface

We address the double bubble problem for the anisotropic Grushin perimeter Pα, α ≥ 0, and the Lebesgue measure in ℝ2, in the case of two equal volumes. We assume that the contact interface between the bubbles lies on either the vertical or the horizontal axis. We first prove existence of minimizers via the direct method by symmetrization arguments and then characterize them in terms of the given area by first variation techniques. Even though no regularity theory is available in this setting, we prove that angles at which minimal boundaries intersect satisfy the standard 120-degree rule up to a suitable change of coordinates. While for α = 0 the Grushin perimeter reduces to the Euclidean one and both minimizers coincide with the symmetric double bubble found in Foisy et al. [Pacific J. Math. 159 (1993) 47–59], for α = 1 vertical interface minimizers have Grushin perimeter strictly greater than horizontal interface minimizers. As the latter ones are obtained by translating and dilating the Grushin isoperimetric set found in Monti and Morbidelli [J. Geom. Anal. 14 (2004) 355–368], we conjecture that they solve the double bubble problem with no assumptions on the contact interface.

Interaction mechanism of double bubbles in hydrodynamic cavitation

2013 ◽  
Vol 22 (3) ◽  
pp. 242-249 ◽  
Author(s):  
Fengchao Li ◽  
Jun Cai ◽  
Xiulan Huai ◽  
Bin Liu
Keyword(s):  
Interaction Mechanism ◽  
Hydrodynamic Cavitation ◽  
Double Bubbles

MATHEMATICS:Why Double Bubbles Form the Way They Do

Science ◽  
2000 ◽  
Vol 287 (5460) ◽  
pp. 1910a-1912 ◽  
Author(s):  
B. Cipra
Keyword(s):  
Double Bubbles ◽  
The Way

On the stability of double bubbles and double drops

2003 ◽  
Vol 262 (1) ◽  
pp. 212-220 ◽  
Author(s):  
Lev A Slobozhanin ◽  
J.Iwan D Alexander
Keyword(s):  
The Stability ◽  
Double Bubbles

scholarly journals From Stable ZnO and GaN Clusters to Novel Double Bubbles and Frameworks

Inorganics ◽  
2014 ◽  
Vol 2 (2) ◽  
pp. 248-263 ◽  
Author(s):  
Matthew Farrow ◽  
John Buckeridge ◽  
C. Catlow ◽  
Andrew Logsdail ◽  
David Scanlon ◽  
...  
Keyword(s):  
Double Bubbles
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