Tri Minh Le (TU Wien)
Abstract: Eikonal equations in metric spaces have strong connections with the local slope operator (or the De Giorgi slope). This talk discusses an analogous model associated with the global slope operator, expressed as $\lambda u + G[u] = \ell$, where $\lambda \geq 0$. The case $\lambda=0$ is naturally related to the so–called discrete weak KAM theory. Under mild assumptions on the metric space $X$ and the given function $\ell$, we establish the well–posedness of this equation. Our techniques further imply a new integration formula based on the global slope operator.