The Lp Minkowski problem for q-torsional rigidity

Abstract

In this paper, we introduce the so-called Lp q-torsional measure for p ∈ R and q > 1 by establishing the Lp variational formula for the q-torsional rigidity of convex bodies without smoothness conditions. Moreover, we achieve the existence of solutions to the Lp Minkowski problem w.r.t. the q-torsional rigidity for discrete measure and general measure when 0 < p < 1 and q > 1.2010 Mathematics Subject Classification. 52A20 52A40.