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 ϵ-regularity criteria involving both excess functionals and nonlinear potentials.
Nonlinear Potential Theory of elliptic systems / Kuusi, Tuomo; Mingione, Giuseppe. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 138:(2016), pp. 277-299. [10.1016/j.na.2015.12.022]
Nonlinear Potential Theory of elliptic systems
Kuusi, Tuomo;Mingione, Giuseppe
2016-01-01
Abstract
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 ϵ-regularity criteria involving both excess functionals and nonlinear potentials.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.