Scaling invariant Sobolev-Lorentz capacity on $\mathbb{R}^{n}$ Serban Costea 31C15Sobolev-Lorentz capacity We develop a capacity theory based on the definition of Sobolev functions on $\mathbf{R}^n$ with respect to the Lorentz norm. Basic properties of capacity, including monotonicity, finite subadditivity and convergence results are included. We also provide sharp estimates for the capacity of balls. Sobolev-Lorentz capacity and Hausdorff measures are related. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3216 10.1512/iumj.2007.56.3216 en Indiana Univ. Math. J. 56 (2007) 2641 - 2670 state-of-the-art mathematics http://iumj.org/access/