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arXiv · 2605.31018

Existence results for nonlinear cone degenerate Laplace equations

Hua Chen·Xiaochun Liu·Yawei Wei·Mengnan Zhang
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Abstract

This paper concerns a class of non-divergence nonlinear elliptic equations driven by the cone degenerate Laplacian, which is motivated by cone calculus. We establish the existence of viscosity solutions by proving the Alexandrov-Bakelman-Pucci and H\"older estimates. Furthermore, we obtain the existence of weak solutions by proving the equivalence between weak solutions and viscosity solutions.

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Hua Chen, Xiaochun Liu, Yawei Wei, Mengnan Zhang. 2026-05-29. Existence results for nonlinear cone degenerate Laplace equations. https://arxiv.org/abs/2605.31018

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