The equivalence of viscosity and distributional subsolutions for convex subequations — a strong Bellman principle

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Abstract

There are two useful ways to extend nonlinear partial differential inequalities of second order beyond the class of C 2 functions: one uses viscosity theory and the other uses the theory of distributions. This paper considers the convex situation where both extensions can be applied. The main result is that under a natural “second-order completeness” hypothesis, the two sets of extensons are isomorphic, in a sense that is made precise.

Keywords

viscosity distributional subsolution solution convex subequation Bellman equation plurisubharmonic 

Mathematical subject classification

35J15 35J60 35J70 
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Copyright information

© Sociedade Brasileira de Matemática 2013

Authors and Affiliations

  1. 1.Department of MathematicsRice UniversityHoustonUSA
  2. 2.Department of MathematicsStony Brook UniversityStony BrookUSA

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