Brunn-Minkowski inequalities for two functionals involving the p-Laplace operator

Abstract

In the family of n-dimensional convex bodies, we prove a Brunn-Minkowski type inequality for the first eigenvalue of the p-Laplace operator, or Poincaré constant, and for a functional extending the notion of torsional rigidity. In the latter case we also characterize equality conditions.

Keywords:

• Brunn-Minkowski inequality
• p-Laplace operator
• Torsional rigidity
• First eigenvalue

Keywords:

• AMS 2000 Subject Classifications: 35J60
• 39B62
• 47J05
• 52A40
• 52C25