The Minkowski problem for the torsional rigidity

By Andrea Colesanti, M. Fimiani. 2008

69 citations recorded by the source corpus.

We prove the existence and uniqueness up to translations of the solution to a Minkowski type problem for the torsional rigidity in the class of open bounded convex subsets of ℝ n . For the existence part we apply the variational method introduced by Jerison in: Adv. Math. 122 (1996), pp. 262-279. Uniqueness follows from the Brunn-Minkowski inequality for the torsional rigidity and corresponding equality conditions.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8d7c1be72e32907d5f2902e1b9207e65d996b6d6

Citations in the corpus

• The logarithmic Minkowski problem (2012, unknown): “, [13], [21], [23], [29], and [31].”
• The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization (2011, unknown): “6] (see also (17) in [7]) we know that Φm(θ)→ Φ0(θ) a.”