- Author
- Michael Ruzhansky (UGent) , Serikbol Shaimardan (UGent) and Kanat Tulenov (UGent)
- Organization
- Abstract
- In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo-Nirenberg type inequality and as its application we show global well-posedness of nonlinear PDEs in the noncommutative Euclidean space. Moreover, we show that the logarithmic Sobolev inequality is equivalent to the Nash inequality for possibly different constants in this noncommutative setting by completing the list in noncommutative Varopoulos's theorem in [37]. Finally, we present a direct application of the Nash inequality to compute the time decay for solutions of the heat equation in the noncommutative setting.
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01JHFDMGEEMFYRY1YRJWSGV865
- MLA
- Ruzhansky, Michael, et al. Sobolev Inequality and Its Applications to Nonlinear PDE on Noncommutative Euclidean Spaces. 2024.
- APA
- Ruzhansky, M., Shaimardan, S., & Tulenov, K. (2024). Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces.
- Chicago author-date
- Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2024. “Sobolev Inequality and Its Applications to Nonlinear PDE on Noncommutative Euclidean Spaces.”
- Chicago author-date (all authors)
- Ruzhansky, Michael, Serikbol Shaimardan, and Kanat Tulenov. 2024. “Sobolev Inequality and Its Applications to Nonlinear PDE on Noncommutative Euclidean Spaces.”
- Vancouver
- 1.Ruzhansky M, Shaimardan S, Tulenov K. Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces. 2024;
- IEEE
- [1]M. Ruzhansky, S. Shaimardan, and K. Tulenov, “Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces,” 2024.
@article{01JHFDMGEEMFYRY1YRJWSGV865, abstract = {{ In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo-Nirenberg type inequality and as its application we show global well-posedness of nonlinear PDEs in the noncommutative Euclidean space. Moreover, we show that the logarithmic Sobolev inequality is equivalent to the Nash inequality for possibly different constants in this noncommutative setting by completing the list in noncommutative Varopoulos's theorem in [37]. Finally, we present a direct application of the Nash inequality to compute the time decay for solutions of the heat equation in the noncommutative setting. }}, author = {{Ruzhansky, Michael and Shaimardan, Serikbol and Tulenov, Kanat}}, language = {{und}}, title = {{Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces}}, year = {{2024}}, }