##### Sesión Ecuaciones Diferenciales y Probabilidad

Diciembre 15, 16:30 ~ 16:50

## On viscosity and weak solutions for non-homogeneous p-Laplace equations

### OCHOA, Pablo

In this talk, we shall discuss the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower order term depending on $x$, $u$ and $\nabla u$. More precisely, we will show that any locally bounded viscosity solution constitutes a weak solution, extending results presented in Juutinen, Lindqvist and Manfredi [2], and Julin and Juutinen [1]. Moreover, we provide a converse statement in the full case under extra assumptions on the data. We will close the talk with applications to Radó type results. References: \begin{itemize} \item[[ 1]] V. Julin, P. Juutinen, \textit{A new proof for the equivalence of weak and viscosity solutions for the p-Laplace equation}. Communications in PDE \textbf{37} 5 (2012), 934-946. \item[[ 2]] P. Juutinen, P. Lindqvist, and J. Manfredi, \textit{On the equivalence of viscosity solutions and weak solutions for a quasilinear equation}, SIAM J. Math. Anal. \emph{33} 3 (2001), 699-717. \item[[ 3]] M. Medina and P. Ochoa, \textit{On viscosity and weak solutions for non-homogeneous p-Laplace equations}. To appear in Advances in Non-linear Analysis. \end{itemize}

Autores: OCHOA, Pablo / Medina, María.