On the isoperimetric problem with respect to a mixed Euclidean–Gaussian density |
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| Authors: | N Fusco F Maggi A Pratelli |
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| Institution: | a Dipartimento di Matematica ed Applicazioni, via Cintia, 80126 Napoli, Italy;b Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy;c Dipartimento di Matematica, Via Ferrata 1, 27100 Pavia, Italy |
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| Abstract: | The isoperimetric problem with respect to the product-type density  on the Euclidean space Rh×Rk 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. |
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| Keywords: | Isoperimetric problem Gaussian density Existence of minimizers |
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