Korean J. Math. Vol. 29 No. 1 (2021) pp.57-64
DOI: https://doi.org/10.11568/kjm.2021.29.1.57

Embedding theorems on the fractional Orlicz-Sobolev spaces

Main Article Content

Tacksun Jung
Q-Heung Choi

Abstract

In this paper we deal with the embedding inclusions on the fractional Orlicz-Sobolev spaces which are crucial roles for studying the theories of the partial differential equations. We get some properties and theories of the embedding inclusions on the fractional Orlicz-Sobolev spaces.



Article Details

Supporting Agencies

Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education Science and Technology

References

[1] E. Azroul, A. Benkirane and M. Srati, Existence of solutions for a nonlocal type problem in fractional Orlicz-Sobolev spaces, preprint (2019). Google Scholar

[2] J. F. Bonder and A. M. Salort, Fractional order Orlicz-Sobolev spaces, Journal of Functional Analysis, https://doi.org/10.1016/j.jfa.2019.04.003 (2019). Google Scholar

[3] Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66, 1383-1406 (2006). Google Scholar

[4] M. Garci´ a −Huidobro, V. K. Le, R. M an´ asevich and K. Schmitt, On principle eigenvalues for quasilinear elliptic differential operators: An Orlicz-Sobolev space setting, Nonlineae Differential Equations Appl. (NoDEA)6, 207-225, (1999). Google Scholar

[5] J. P. Gossez, Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients, Trans. Amer. Math. Soc. 190, 163-205 (1974). Google Scholar

[6] M. Hsini, N. Irzi and Kh. Kefi, On a fractional problem with variable exponent, Proceedings of the Romanian Academy-Series A: Mathematics, Physics, Technical Sciences, Information Science, (2019). Google Scholar

[7] U. Kaufmann, J. D. Rossi and R. Vidal, Fractional Sobolev spaces with variable exponents and p(x)−Laplacians, Electron. J. Qual. Theory Differ. Equ. 76, 1-10 (2017). Google Scholar

[8] M. M ihˇ ailescu and V. Rˇ adulescu, Neumann problems associated to nonhomogeneous differential operators in Orlicz-Sobolev spaces, Ann. Inst. Fourier, 58, 2087-2111 (2008). Google Scholar

[9] L. M. Pezzo and J. D. Rossi, Trace for fractional Sobolev spaces with variables exponents, arXiv: 1704.02599. Google Scholar

[10] M. Ruzicka, Electrorheological Fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin,(2002). Google Scholar

[11] A. M. Salort, A fractional Orlicz-Sobolev eigenvalue problem and related Hardy inequalities, arXiv e-prints, arXiv:1807.03209 (2018). Google Scholar

[12] C. Zhang and X. Zhang, Renormalized solutions for the fractional p(x)−Laplacian equation with L1 data, arXiv: 1708.04481v1. Google Scholar

[13] V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk SSSR Ser. Mat. 50, no. 4, 675-710 (1986); English transl., Math. USSR-Izv 29, no. 1, 33-66 (1987). Google Scholar