| Optimal regularity of viscosity solutions of fully nonlinear singular equations and their limiting free boundary problems, Mat. Contemp., submitted for publication (2009) | |||||||||||||||
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| Abstract. In the present paper, we start the journey of investigation into fully nonlinear elliptic singular equations of the form F (D 2 u, x) = βε(uε), where βε(uε) converges to the Dirac delta measure δ0. We show optimal regularity, uniform in ε, as well as H 1 compactness for Bellman’s singular equations. We also provide a complete picture of limiting one-dimensional profiles. The study of further geometric-measure properties as well as smoothness of the general limiting free boundary problem is currently in progress [16]. 1. | |||||||||||||||
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