| Abstract: |
| We deal with the asymptotic behavior as $p\to 1^+$ of weak solutions to nonlinear Dirichlet problems modeled by
\begin{equation*}
\begin{cases}
-\Delta_p u + |u|^{p-1}u = -\text{\text{div}}\left(|u|^{p-2}u E(x)\right) + |\nabla u|^{p-2}\nabla u\cdot F(x) + f(x) & \text{ in }\Omega, \
u=0 & \text{ on }\partial\Omega,
\end{cases}
\end{equation*}
where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge 2$). We focus on the a priori estimates depending on the norm of the Lebesgue functions $E,F$ and $f$ which guarantee the existence of a limit problem in the framework of functions of bounded variation.
This is a joint work with Francescantonio Oliva. |
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