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arXiv · 2501.04909

On the Heat equation involving a Grushin operator in Marcinkiewcz spaces

Alessia E. Kogoj·Maria E. Lima·Arlúcio Viana
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Abstract

In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator $$ \Delta_{\mathcal{G}}=\dfrac{1}{2}\left(\Delta_{x}+|x|^2\Delta_{y}\right) $$ in Marcinkiewicz spaces. Furthermore, we provide sufficient conditions for the existence of positive, symmetric, and self-similar solutions.

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Alessia E. Kogoj, Maria E. Lima, Arlúcio Viana. 2025-01-09. On the Heat equation involving a Grushin operator in Marcinkiewcz spaces. https://doi.org/10.1007/s13163-025-00538-4

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