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arXiv · 2412.21078

A Compactness Condition for the Theorem of Sums in a Class of Non-Uniformly Elliptic PDEs

Daniel Maienshein
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Abstract

In the theory of viscosity solutions for second-order, degenerate elliptic PDEs, the Ishii-Lions method is a commonly used strategy, and the theorem of sums is the main analytical tool. As noted by Porretta and Priola, uniformly elliptic PDEs admit a version of the theorem of sums without the squared term due to a compactness argument. Here, we introduce a larger class of PDEs for which the compactness argument holds.

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Daniel Maienshein. 2024-12-30. A Compactness Condition for the Theorem of Sums in a Class of Non-Uniformly Elliptic PDEs. https://arxiv.org/abs/2412.21078

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