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"In this article we study two classical potential-theoretic problems in convex geometry. The first problem is an inequality of Brunn-Minkowski type for a nonlinear capacity, CapA, where A-capacity is associated with a nonlinear elliptic PDE whose structure is modeled on the p-Laplace equation and whose solutions in an open set are called A-harmonic"--

Minkowski geometry. --- Inequalities (Mathematics) --- Nonlinear theories. --- Elliptic functions. --- Harmonic functions. --- Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations. --- Potential theory -- Higher-dimensional theory -- Potentials and capacities, extremal length. --- Difference and functional equations -- Functional equations and inequalities -- Functional inequalities, including subadditivity, convexity, etc.. --- Convex and discrete geometry -- General convexity -- Inequalities and extremum problems. --- Partial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations. --- Convex and discrete geometry -- General convexity -- Convex sets in $n$ dimensions (including convex hypersurfaces). --- Partial differential equations -- Elliptic equations and systems -- Quasilinear elliptic equations with $p$-Laplacian.