Measuring the level sets of anisotropic homogeneous functions

Measuring the level sets of anisotropic homogeneous functions In this note we investigate some basic properties of the level sets of functions which are homogeneous with respect to nonisotropic dilations. In particular we obtain a formula for the volume of the level sets in terms of the area on the level surfaces. We relate the results to some well known mean value formulas for solutions of PDE’s. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Measuring the level sets of anisotropic homogeneous functions

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0087-3
Publisher site
See Article on Publisher Site

Abstract

In this note we investigate some basic properties of the level sets of functions which are homogeneous with respect to nonisotropic dilations. In particular we obtain a formula for the volume of the level sets in terms of the area on the level surfaces. We relate the results to some well known mean value formulas for solutions of PDE’s.

Journal

PositivitySpringer Journals

Published: Sep 28, 2010

References

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