Advances in Calculus of Variations
Advances in Calculus of Variations
Given two annuli ๐ธ โข ( r , R ) {\mathbb{A}(r,R)} and ๐ธ โข ( r โ , R โ ) {\mathbb{A}(r_{\ast},R_{\ast})} , in ๐ 3 {\mathbf{R}^{3}} equipped with the Euclidean metric and the weighted metric | y | - 2 {\lvert y\rvert^{-2}} , respectively, we minimize the Dirichlet integral, โฆ