Nonlinear Potential Theory of elliptic systems

We give a summary of recent results from Nonlinear Potential Theory, focusing on linear and nonlinear potential estimates of solutions to non-homogeneous equations and systems. We start with the cases of quasilinear, possibly degenerate equations of pp-Laplacian type, and, passing through fully nonlinear elliptic equations, finally move to systems. In this last case we describe recent results implying potential estimates for the pp-Laplacian system. Finally, we describe results bridging Nonlinear Potential Theory and classical partial regularity theory for general elliptic systems. The main outcomes are new εε-regularity criteria involving both excess functionals and nonlinear potentials.