Special Session 80: Functional inequalities and PDEs

On the superposition and the Phragm\`{e}n-Lindel\{o}f principles for the $p$-Laplacian
Pier Domenico Lamberti
University of Padova
Italy
Co-Author(s):    Vitaly Moroz
Abstract:
We prove a Phragm\`{e}n-Lindel\{o}f type comparison principle for equations driven by the $p$-Laplacian on exterior domains, in the presence of a negative potential and for $p \geq 2$. As a consequence, we obtain upper and lower bounds for subsolutions and supersolutions in the setting of Hardy-type potentials. The argument is based on a new superposition principle for the $p$-Laplacian. The results are part of a joint work with Vitaly Moroz.