Year: 2024
Type: article
Abstract: We consider integrals in the sense of Choquet with respect to the $$\delta $$ δ -dimensional Hausdorff content for continuously differentiable functions defined on open, connected sets in the Euclidean n-space, $$n\ge 2$$ n ≥ 2 , $$0<\delta \le n$$ 0 < δ ≤ n . In particular, for these functions we prove Sobolev inequalities in the limiting case $$p=\delta /n$$ p = δ / n and in the case $$p>\delta $$ p > δ , here p is the integrability exponent of the absolute value of the gradient of any given function. The results complement previously known Poincaré–Sobolev and Morrey inequalities.
Source: La Matematica
Authors: Petteri Harjulehto, Ritva Hurri-Syrjänen
Institution: University of Helsinki
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Helsingin Yliopisto
OpenAlex ID: W4402604624