Browsing by Author "Zagatti, Sandro"

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    Compactness by maximality
    (2011) Zagatti, Sandro; Mathematics
    We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.