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arXiv · 1301.4914

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

F. Reese Harvey·H. Blaine Lawson Jr
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Abstract

There are two useful ways to extend nonlinear partial differential inequalities of second order: 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 extensions are isomorphic, in a sense that is made precise.

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F. Reese Harvey, H. Blaine Lawson Jr. 2013-01-21. The equivalence of viscosity and distributional subsolutions for convex subequations - a strong Bellman principle. https://arxiv.org/abs/1301.4914

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