Published Paper

Inserted: 13 jul 2018
Last Updated: 13 jul 2018

Journal: Journal de Mathématiques Pures et Appliquées
Year: 2014
Doi: https://www.sciencedirect.com/science/article/pii/S0021782413001748

Abstract:

We study the existence of solutions to the equation $-\Delta_pu+g(x,u)=\mu$ when $g(x,.)$ is a nondecreasing function and $\mu$ a measure. We characterize the good measures, i.e. the ones for which the problem has a renormalized solution. We study particularly the cases where $g(x,u)=
x
^{-\beta}
u
^{q-1}u$ and $g(x,u)=\text{sign }(u)(e^{\tau
u
^\lambda} -1)$. The results state that a measure is good if it is absolutely continuous with respect to an appropriate Lorentz-Bessel capacities.

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