On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space
- Hewett, Dave
- Moiola, Andrea
DOIAbstract
This paper concerns the following question: given a subset E of Rn with empty interior and an integrability parameter 1<p<infinity, what is the maximal regularity s in R for which there exists a non-zero distribution in the Bessel potential Sobolev space Hs,p(Rn) that is supported in E? For sets of zero Lebesgue measure we apply well-known results on set capacities from potential theory to characterise the maximal regularity in terms of the Hausdorff dimension of E, sharpening previous results. Furthermore, we provide a full classification of all possible maximal regularities, as functions of p, together with the sets of values of p for which the maximal regularity is attained, and construct concrete examples for each case. Regarding ...
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