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arXiv · 2311.09964

On Choquet integrals and Sobolev type inequalities

Petteri Harjulehto·Ritva Hurri-Syrjänen
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Abstract

We consider integrals in the sense of Choquet with respect to the $\delta$-dimensional Hausdorff content for continuously differentiable functions defined on open, connected sets in the Euclidean $n$-space, $n\geq 2$, $0<\delta\le n$. In particular, for these functions we prove Sobolev inequalities in the limiting case $p=\delta /n$ and in the case $p>\delta$, here $p$ is the integrability exponent of the absolute value of the gradient of any given function. The results complement previously known Poincar\'e-Sobolev and Morrey inequalities.

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Petteri Harjulehto, Ritva Hurri-Syrjänen. 2023-11-16. On Choquet integrals and Sobolev type inequalities. https://arxiv.org/abs/2311.09964

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