Sobolev inequalities with variable exponent attaining the values $1$ and $n$
By Petteri Harjulehto, P. Hasto. 2008
48 citations recorded by the source corpus.
We study Sobolev embeddings in the Sobolev space $W^{1,p(\cdot)}(\Omega)$ with variable exponent satisfying $1\leqslant p(x) \leqslant n$. Since the exponent is allowed to reach the values $1$ and $n$, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which features a space of exponential type integrability instead of $L^\infty$ at the upper end.
Subfields: Applied Mathematics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/8e3028ab5b98efe14b1a3a31773de755ef1fd19c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Patrizia Pucci
- G. Autuori
- Binlin Zhang
- Mingqi Xiang
- Giovanni Molica Bisci
- Vicentiu D. Rădulescu
- A. Fiscella
- Luca Vilasi
In Mechanics of Materials
Citations in the corpus
- Global Nonexistence for Nonlinear Kirchhoff Systems (2010, background): “Details, extensions and further references can be found in [10,12–16].”