| Abstract: |
| We study a class of degenerate fully nonlinear elliptic equations, consisting of a pure equation and an associated transmission-type free boundary problem. First, we propose a regularization of the pure equation and develop a numerical method for the resulting regularized problem. This regularization also plays a role in ensuring the monotonicity of the numerical scheme. We prove that the method is monotone, consistent, and stable. Consequently, the Barles-Souganidis framework guarantees the convergence of the numerical approximation. Once the numerical treatment of the pure equation is established, we show how a similar approach can be extended to the free boundary transmission problem. Finally, we present numerical experiments that support the theoretical results. This work has been done in collaboration with Edgard Pimentel. |
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