Isoperimetric problems in sectors with density
By A. D'iaz, Nate Harman, S. Howe, D. Thompson. 2010
47 citations recorded by the source corpus.
We consider the isoperimetric problem in planar sectors with density $r^{p}$, and with density $a>1$ inside the unit disk and $1$ outside. We characterize solutions as a function of sector angle. We also solve the isoperimetric problem in $\mathbb{R}^{n}$ with density $r^{p},\; p<0$.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/33c0b3708e6ba3ef0011d2306887ccd61ccef76e
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In Applied Mathematics
- Lenka Slav'ikov'a
- L. Pick
- Andrea Cianchi
- Emanuel Milman
- Liran Rotem
- Joaquim Martín
- Mario Milman
- Iwona Chlebicka
In Computational Theory and Mathematics
- Andrea Cianchi
- Liran Rotem
- L. Pick
- Emanuel Milman
- Iwona Chlebicka
- Robert J. Berman
- G. Lu
- Nguyen Huong Lam
Citations in the corpus
- Complemented Brunn–Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures (2013, result): “ isoperimetric minimizers has been established by Can˜ete and Rosales [9, 10]. When w(x) = |x| 1 p and K is the Euclidean ball, Theorem 1.3 was previously obtained by D´ıaz, Harman, Howe and Thompson [13]. A more general result has been established by Howe [19], see Theorem 1.4 below. The proof of T”
- Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “Let us limit ourselves to mentioning that, besides those quoted above, recent contributions on isoperimetric problems in (domains in) R endowed with a measure ν include [17,35,42,79].”