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Improved bounds for solutions of Φ-laplacians

Arriagada W., Huentutripay J.

Opuscula Mathematica

2018

Vol. 38, no. 6

765--777

In this short paper we prove a parametric version of the Harnack inequality for Φ-Laplacian equations. In this sense, the estimates are optimal and represent an improvement of previous bounds for this kind of operators.

Potential theory for Lévy stable processes

Bogdan K., Stós A., Sztonyk P.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 3

361-372

We investigate properties of functions that are harmonic with respect to symmetric stable processes which are not necessarily rotation invariant. We prove the Harnack inequality and the boundary Harnack principle for a Lipschitz domain. To obtain this we use Poisson kernel estimates. We also give an estimate concerning the rate of decay of harmonic functions near the boundary of the domain.