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Solvability of Uniformly Elliptic Fully Nonlinear PDE

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Abstract

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the Hamilton–Jacobi–Bellman–Isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.

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Authors and Affiliations

  1. UFR SEGMI, Université Paris 10, 92001, Nanterre Cedex, France

    Boyan Sirakov

  2. CAMS, EHESS 54 bd Raspail, 75270, Paris Cedex 06, France

    Boyan Sirakov

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  1. Boyan Sirakov
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Correspondence to Boyan Sirakov.

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Communicated by P.-L. Lions

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Sirakov, B. Solvability of Uniformly Elliptic Fully Nonlinear PDE. Arch Rational Mech Anal 195, 579–607 (2010). https://doi.org/10.1007/s00205-009-0218-9

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  • DOI: https://doi.org/10.1007/s00205-009-0218-9

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