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arXiv · 2110.12420

Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups

Prashanta Garain·Alexander Ukhlov
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Abstract

In this article we study singular subelliptic $p$-Laplace equations and best constants in Sobolev inequalities on nilpotent Lie groups. We prove solvability of these subelliptic $p$-Laplace equations and existence of the minimizer of the corresponding variational problem. It leads to existence of the best constant in the corresponding $(q,p)$-Sobolev inequality, $0<q<1$, $1<p<\nu$.

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Prashanta Garain, Alexander Ukhlov. 2021-10-24. Singular subelliptic equations and Sobolev inequalities on nilpotent Lie groups. https://arxiv.org/abs/2110.12420

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