Nonlinear Potential Theory of elliptic systems

作者：Kuusi Tuomo; Mingione Giuseppe^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2016, 138: 277-299.

DOI：10.1016/j.na.2015.12.022

• Nonlinear Potential Theory
• Regularity
• Elliptic equations

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 p-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 p-Laplacian system. Finally, we describe results bridging Nonlinear Potential Theory and classical partial regularity theory for general elliptic systems. The main outcomes are new epsilon-regularity criteria involving both excess functionals and nonlinear potentials.

• 出版日期2016-6