Sharp inequalities for solutions to elliptic problems with mixed boundary conditions
Apparaît dans la collection : Shape Optimization, Spectral Geometry and Calculus of Variations / Optimisation de forme, géométrie spectrale et calcul des variations
We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on L1 comparison) between solutions to an elliptic partial differential equation on a smooth bounded set Ω with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as Ω. This includes for instance mixed problems.
