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

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.
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2840762
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