𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Weighted isoperimetric inequalities on ℝn and applications to rearrangements

✍ Scribed by M. Francesca Betta; Friedemann Brock; Anna Mercaldo; M. Rosaria Posteraro

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
353 KB
Volume
281
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We study isoperimetric inequalities for a certain class of probability measures on ℝ^n^ together with applications to integral inequalities for weighted rearrangements. Furthermore, we compare the solution to a linear elliptic problem with the solution to some “rearranged” problem defined in the domain {x: x~1~ < α (x~2~, …, x~n~)} with a suitable function α (x~2~, …, x~n~). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

On the InclusionH2(Un)&#xa0;⊂&#xa0;H2n(B
On the InclusionH2(Un)&#xa0;⊂&#xa0;H2n(Bn) and the Isoperimetric Inequality
✍ Miroslav Pavlović; Milutin R Dostanić 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 113 KB

Let U n and B n be the unit polydisc and the unit all in ‫ރ‬ n , respectively. We 2 Ž n . that the n norm of the inclusion is equal to one. If f depends on one variable only, then the Ž . result reduces to an inequality of isoperimetric type due to Carleman n s 2 and Ž . Burbea n ) 2 .

Nonlinear Fredholm Operators with Noncom
Nonlinear Fredholm Operators with Noncompact Fibers and Applications to Elliptic Problems on RN
✍ Patrick J Rabier 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 202 KB

Under suitable conditions, an equation F(x)=y between Banach spaces involving a nonlinear Fredholm mapping F of nonnegative index is shown to have a noncompact and hence infinite set of solutions for almost every y for which the equation is solvable. The proof of this nonuniqueness (but not existenc