W2, p Estimates for the Monge–Ampère Equation

  • Cristian E. Gutiérrez
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 89)


Our purpose in this chapter is to prove Caffarelli’s interior L p estimates for second derivatives of solutions to the Monge–Ampère equation. That is, solutions u to Mu = f with f positive and continuous have second derivatives in L p , for 0 < p < , Theorem 6.4.2.


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Cristian E. Gutiérrez
    • 1
  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA

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