A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf
.
On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space
2017
Analysis and Applications
This paper concerns the following question: given a subset E of R n with empty interior and an integrability parameter 1 < p < ∞, what is the maximal regularity s ∈ R for which there exists a non-zero distribution in the Bessel potential Sobolev space H s,p (R n ) 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
doi:10.1142/s021953051650024x
fatcat:kyycdsj7dbalncvlqa4vznojiq