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arXiv · 2209.12357

Non-local equations and optimal Sobolev inequalities on compact manifolds

Carolina Rey·Nicolas Saintier
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Abstract

This paper deals with fractional Sobolev spaces on a compact Riemannian manifold. We prove a Sobolev inequality in the critical range with an optimal constant for these fractional Sobolev spaces. We use this result to study the existence of a non-trivial solution for equations driven by a non-local integro-differential operator $\mathcal{L}_{\mathcal{K}}$ with critical non-linearity.

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Carolina Rey, Nicolas Saintier. 2022-09-26. Non-local equations and optimal Sobolev inequalities on compact manifolds. https://arxiv.org/abs/2209.12357

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