Radially increasing minimizing surfaces or deformations under pointwise constraints on positions and gradients Original Research Article

In this paper, we prove existence of radially symmetric minimizersuA(x)=UA(|x|)uA(x)=UA(|x|), having UA(⋅)UA(⋅)AC monotone and View the MathML sourceℓ∗∗(UA(⋅),0) increasing, for the convex scalar multiple integral equation(∗ ) View the MathML source∫BRℓ∗∗(u(x),|∇u(x)|ρ1(|x|))⋅ρ2(|x|)dx Turn MathJax on among those u(⋅)u(⋅) in the Sobolev spaceView the MathML sourceA+W01,1(BR). Here, |∇u(x)||∇u(x)| is the Euclidean norm of the gradient vector and BRBR is the ballball View the MathML source{x∈Rd:|x|