Isoperimetric Inequalities for Extremal Sobolev Functions

Jesse Ratzkin; Tom Carroll

doi:10.1007/978-3-319-21284-5_13

Isoperimetric Inequalities for Extremal Sobolev Functions

Jesse Ratzkin
, Tom Carroll

School of Mathematical Sciences

University of Cape Town

Research output: Contribution to journal › Article › peer-review

Abstract

Let be a bounded domain with boundary of class. One can measure various geometric and physical quantities attached to, such as volume, perimeter, diameter, in-radius, torsional rigidity, and principal frequency. The first chapter of [16] contains a long list of such interesting quantities, as well as their values for standard shapes such as disks, rectangles, strips, and triangles.

Original language	English
Pages (from-to)	67-71
Number of pages	5
Journal	Trends in Mathematics
Volume	3
DOIs	https://doi.org/10.1007/978-3-319-21284-5_13
Publication status	Published - 2015

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title = "Isoperimetric Inequalities for Extremal Sobolev Functions",

abstract = "Let be a bounded domain with boundary of class. One can measure various geometric and physical quantities attached to, such as volume, perimeter, diameter, in-radius, torsional rigidity, and principal frequency. The first chapter of [16] contains a long list of such interesting quantities, as well as their values for standard shapes such as disks, rectangles, strips, and triangles.",

author = "Jesse Ratzkin and Tom Carroll",

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AB - Let be a bounded domain with boundary of class. One can measure various geometric and physical quantities attached to, such as volume, perimeter, diameter, in-radius, torsional rigidity, and principal frequency. The first chapter of [16] contains a long list of such interesting quantities, as well as their values for standard shapes such as disks, rectangles, strips, and triangles.

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JO - Trends in Mathematics

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ER -

Isoperimetric Inequalities for Extremal Sobolev Functions

Abstract

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