Abstract
We consider the Dirichlet boundary value problem for a singular elliptic PDE like F[u] = p(x)u −μ, where p, μ ≥ 0, in a bounded smooth domain of \({\mathbb{R}^n}\) . The nondivergence form operator F is assumed to be of Hamilton–Jacobi–Bellman or Isaacs type. We establish existence and regularity results for such equations.
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Felmer, P., Quaas, A. & Sirakov, B. Existence and regularity results for fully nonlinear equations with singularities. Math. Ann. 354, 377–400 (2012). https://doi.org/10.1007/s00208-011-0741-5
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DOI: https://doi.org/10.1007/s00208-011-0741-5