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arXiv · 1501.05585

On the viscosity solutions to Trudinger's equation

Tilak Bhattacharya·Leonardo Marazzi
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Abstract

We study the existence of positive viscosity solutions to Trudinger's equation for cylindrical domains $Ω\times[0, T)$, where $Ω\subset \mathbb{R}^n,\;n\ge 2,$ is a bounded domain, $T>0$ and $2\leq p<\infty$. We show existence for general domains $Ω,$ when $n<p<\infty$. For $2\leq p\leq n$, we prove existence for domains $Ω$ that satisfy a uniform outer ball condition. We achieve this by constructing suitable sub-solutions and super-solutions and applying Perron's method.

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Tilak Bhattacharya, Leonardo Marazzi. 2015-01-22. On the viscosity solutions to Trudinger's equation. https://doi.org/10.1007/s00030-015-0315-4

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