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Existence and regularity results for fully nonlinear equations with singularities

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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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Authors and Affiliations

  1. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile

    Patricio Felmer

  2. Departamento de Matemática, Universidad Santa María, Casilla V-110, Avda. España 1680, Valparaíso, Chile

    Alexander Quaas

  3. UFR SEGMI, Université de Paris Ouest, 92001, Nanterre Cedex, France

    Boyan Sirakov

  4. CAMS, EHESS, 190-198, avenue de France, 75244, Paris Cedex 13, France

    Boyan Sirakov

Authors
  1. Patricio Felmer
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  2. Alexander Quaas
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  3. Boyan Sirakov
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Correspondence to Boyan Sirakov.

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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

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