Abstract
Let Gλ, λ > 0, be a Grushin type operator on \(\mathbb{R}^{n}\times\mathbb{R}^{m}\). In this paper, we will first establish existence and uniqueness for the p-Laplace equation for Gλ, then we prove the regularity of solutions. In order to prove our results, we will get the Harnack inequality for Gλ, which maybe has independent interest.
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Supported by the Fundamental Research Funds for the Central Universities (Grant No. 500422107) 1) Corresponding author
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Huang, J.Z., Yang, X.X. P-Laplace Equation for the Grushin Type Operator. Acta. Math. Sin.-English Ser. 39, 923–938 (2023). https://doi.org/10.1007/s10114-023-1213-z
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DOI: https://doi.org/10.1007/s10114-023-1213-z