Circular symmetrization and extremal Robin conditions
Abstract
We study the average temperature in a homogeneous disk subject to uniform heating in its interior and Newton's law of cooling, hv+∂ v/∂ n=0, on its boundary. More precisely, among those h taking values in a prescribed interval, and of prescribed mean, we identify the minimizer and a maximizer of the average temperature. The latter characterization makes use of circular symmetrization. We include an elementary proof of the fact that such symmetrization does not increase the Dirichlet energy of any H1 function on the disk.
- Publication:
-
Zeitschrift Angewandte Mathematik und Physik
- Pub Date:
- 1999
- DOI:
- 10.1007/s000330050152
- Bibcode:
- 1999ZaMP...50..301C