Brunn-Minkowski inequality

The Brunn–Minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators

We prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a Brunn-Minkowski type inequality on the class of open bounded sets in satisfying a uniform exterior sphere condition. In particular the result applies to the (possibly normalized) p-Laplacian, and to the minimal Pucci operator.

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