Naslov
Hausdorff dimension of singular sets of Sobolev functions and applications

Autori
Žubrinić, Darko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Conferences abstracts, ISAAC, July 25-30, 2005, University of Catania, Italy / Wengel, Barbara G. - Catania : Dipartimento di Matematica e Informatica, 2005

Skup
The 5th ISAAC Congress

Mjesto i datum
Catania, Italija, 25.07.2005. - 30.07.2005

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Sobolev function; singular sets; Hausdorff dimension

Sažetak
We are interested in Sobolev functions with large singular sets in the sense of Hausdorff dimension. For functions in $W^{; ; ; k, p}; ; ; (R^N)$, $kp<N$, we find that the optimal bound is $N-kp$. Moreover, the bound is achieved, that is, there exists a class of maximally singular Sobolev functions. Similar results have been obtained for Besov spaces and Lizorkin-Triebel spaces. We describe a class of $p$-Laplace equations such that their weak solutions are singular on a prescribed fractal set having large Hausdorff dimension.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA