Some Applications to Lebesgue Points in Variable Exponent Lebesgue Spaces

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2009
Yayıncı: Çankaya Üniversitesi

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,

[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.