On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density - Fusco, Nicola; Maggi, Francesco; Pratelli, Aldo (Journal of Functional Analysis, 2011)
The isoperimetric problem with respect to the product-type density e-vertical bar x vertical bar/2 dx dy on the Euclidean space R(h) x R(k) is studied. In particular, existence, symmetry and regularity of minimizers is proved. In the special case k = 1, also the shape of all the minimizers is derived. Finally, a conjecture about the minimality of large cylinders in the case k > 1 is formulated. (C) 2011 Elsevier Inc. All rights reserved.
Keywords: Isoperimetric problem; Gaussian density; Existence of minimizers