We show the counter-intuitive fact that some weighted isoperimetric problems on the half-space $ mathbb{R}^N _+ $, for which half-balls centered at the origin are stable, have no solutions. A particular case is the measure $dmu = x_N ^{alpha } , dx$, with $alpha in (-1,0)$. Some results on stability and nonexistence for weighted isoperimetric problems on $mathbb{R}^N $ are also obtained.
Some Weighted Isoperimetric Problems on ${mathbb {R}}^N _+ $ with Stable Half Balls Have No Solutions / Brock, F.; Chiacchio, F.. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - 26:1(2020), pp. 1-19. [10.1007/s00041-019-09723-8]
Some Weighted Isoperimetric Problems on ${mathbb {R}}^N _+ $ with Stable Half Balls Have No Solutions
Chiacchio, F.
2020
Abstract
We show the counter-intuitive fact that some weighted isoperimetric problems on the half-space $ mathbb{R}^N _+ $, for which half-balls centered at the origin are stable, have no solutions. A particular case is the measure $dmu = x_N ^{alpha } , dx$, with $alpha in (-1,0)$. Some results on stability and nonexistence for weighted isoperimetric problems on $mathbb{R}^N $ are also obtained.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
