Measuring the level sets of anisotropic homogeneous functions
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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.
KeywordsHomogeneous functions Volume of level sets Mean values formula Euler formula
Mathematics Subject Classification (2000)31C99 26B15
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- 2.Evans, L.C.: Partial differential equations, graduate studies in mathematics, vol. 19. American Mathematical Society, Providence, RI (1998)Google Scholar
- 6.Pokrovskiĭ A.V.: Mean value theorems for solutions of linear partial differential equations. Mat. Zametki 64(2), 260–272 (1998)Google Scholar