Nodal sets for "broken" quasilinear pdes

  title={Nodal sets for "broken" quasilinear pdes},
  author={Sunghan Kim and Ki-ahm Lee and Henrik Shahgholian},
  journal={Indiana University Mathematics Journal},
We study the local behavior of the nodal sets of the solutions to elliptic quasilinear equations with nonlinear conductivity part, \begin{equation*} \operatorname{div}(A_s(x,u)\nabla u)=\operatorname{div}{\vec f}(x), \end{equation*} where $A_s(x,u)$ has "broken" derivatives of order $s\geq 0$, such as \begin{equation*} A_s(x,u) = a(x) + b(x)(u^+)^s, \end{equation*} with $(u^+)^0$ being understood as the characteristic function on $\{u>0\}$. The vector ${\vec f}(x)$ is assumed to be $C^\alpha… 

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