Some Applications to Lebesgue Points in Variable Exponent Lebesgue Spaces

Year 2010, Volume: 7 Issue: 2, - , 01.04.2010

Rabil A. Mashiyev

https://izlik.org/JA95WH86ME

Abstract

Some corollaries of Lebesgue’s regular points which are useful in the theory of
optimal control for distributed parameter systems are proved. 

Keywords

Variable exponent Lebesgue spaces , Lebesgue regular points , optimal control

References

• [1] O. M. Buhrii and R. A. Mashiyev, Uniqueness of solutions of the parabolic variational inequality with variable exponent of nonlinearity, Nonlinear Anal.-Theor. 70 (2009), 2325–2331.
• [2] A. V. Fursikov, Optimal Control of Distributed Systems. Theory and Applications, American Mathematical Society, Boston, MA 2000.
• [3] O. Kov´aˇcik and J. R´akosn´ık, On spaces L^p(x) and W^k,p(x) , Czech. Math. J. 41 (1991), 592–618.
• [4] R. Mashiyev, Some properties of variable Sobolev capacity, Taiwan. J. Math. 12 (2008), 671–678.
• [5] A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems, Nauka, Moscow 1974.
• [6] P. Harjulehto and P. H¨ast¨o, Lebesgue points in variable exponent spaces, Ann. Acad. Sci. Fenn.-M. 29 (2004), 295–306.
• [7] M. R˚uˇziˇcka, Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, 2000.
• [8] X. Fan and D. Zhao, On the spaces L^p(x) (Ω) and W^m,p(x) (Ω), J. Math. Anal. Appl. 263 (2001), 424–446.