References
- Zhikov , V . 1987 . Averaging of functionals of the calculus of variations and elasticity theory . Math. USSR-Izv , 29 : 675 – 710 . 877
- Zhikov , V . 1995 . On Lavrentiev's phenomenonong . Russ. J. Math. Phys. , 3 : 249 – 269 .
- Kováčik , O and Rákosník , J . 1991 . On spaces L p(x) and W 1, p(x) . Czechoslovak Math. J. , 41 ( 116 ) : 592 – 618 .
- Samko , S . 1998 . Convolution and potential type operators in L p(x)(R n ) . Integr. Transform. Spec. Funct. , 7 ( 3–4 ) : 261 – 284 .
-
Samko.
,
S
.
2000
.
Denseness of
in the generalized Sobolev spaces W M,P(X)(ℝ N ), in Direct and inverse problems of mathematical physics , ed., International Society for Analysis, its Applications and Computation, Vol. 5, R.P. Gilbert, J. Kajiwara, and Y.S. Xu, eds., Kluwer Academic Publishers, Dordrecht : D.E. Newark . pp. 333–342
- Rajagopal , K and Růžička , M . 1996 . On the modeling of electrorheological materials . Mech. Res. Commun. , 23 ( 4 ) : 401 – 407 . 3, 463
- Zhikov , V . 2008 . Solvability of the three-dimensional thermistor problem . Proc. Steklov Inst. Math. , 261 ( 1 ) : 101 – 114 .
- Acerbi , E and Mingione , G . 2000 . Functionals with p(x)-growth and regularity . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. , 11 : 169 – 174 .
- Acerbi , E and Mingione , G . 2001 . Regularity results for a class of functionals with non-standard growth . Arch. Ration. Mech. Anal. , 156 : 121 – 140 .
- Acerbi , E and Mingione , G . 2002 . Regularity results for electrorheological fluids: The stationary case . C. R. Acad. Sci. Paris , 334 : 817 – 822 .
- Diening , L . 2004 . Maximal function on generalized Lebesgue spaces L p(·) . Math. Inequal. Appl. , 7 ( 2 ) : 245 – 254 .
- Nekvinda , A . 2004 . Hardy–Littlewood maximal operator on L p(x)(ℝ n ) . Math. Inequal. Appl. , 7 : 255 – 266 .
- Cruz-Uribe , D , Fiorenza , A , Martell , JM and Pérez , C . 2006 . The boundedness of classical operators in variable L p spaces . Ann. Acad. Sci. Fenn. Math. , 31 ( 1 ) : 239 – 264 .
- Diening , L , Harjulehto , P , Hästö , P and Růžička , M . 2011 . Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, Vol. 2017 , Berlin : Springer .
- Lions , JL . 1969 . Quelques Méthodes de Résolution des Problèmes aux Limites Non linéaires , Paris : Dunod .
- Ladyzhenskaya , OA . 1969 . The Mathematical Theory of Viscous Incompressible Flow , New York : Gordon and Breach .
- Růžička , M . 2000 . Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, Vol. 1748 , Berlin : Springer .
- Antontsev , S and Shmarev , S . 2007 . Parabolic equations with anisotropic nonstandard growth conditions . Free Bound. Probl. , 60 : 33 – 44 .
- Antontsev , S and Shmarev , S . 2009 . Anisotropic parabolic equations with variable nonlinearity . Publ. Mat. , 53 ( 2 ) : 355 – 399 .
- Nägele , P . 2009 . “ Monotone operators in spaces with variable exponents ” . In Diploma thesis , University of Freiburg .
- Alkhutov , Y and Zhikov , V . 2010 . Existence theorems for solutions of parabolic equations with variable order of nonlinearity . Proc. Steklov Inst. Math. , 270 : 1 – 12 .
- Gajewski , H , Gröger , K and Zacharias , K . 1974 . Nichtlineare Operatorgleichungen und Operator differentialgleichungen , Berlin : Akademie-Verlag .
- Droniou , J . 2001 . Intégration et Espaces de Sobolev a Valeurs Véctorielles , Marseille : Lecture Notes, Université de Provence .
- Zeidler , E . 1989 . Nonlinear Functional Analysis and its Applications: Part 2 B: Nonlinear Monotone Operators , Berlin : Springer .
- Růžička , M . 2004 . Nichtlineare Funktionalanalysis , Berlin : Springer .
- Diening , L . 2007 . Lebesgue and Sobolev Spaces with Variable Exponent , Germany : Habilitationsschrift, University of Freiburg .
- Diening , L and Růžička , M . 2003 . Calderón-Zygmund operators on generalized Lebesgue spaces L p(·) and problems related to fluid dynamics . J. Reine Angew. Math. , 563 : 197 – 220 .
- Stein , EM . 1970 . Singular integrals and differentiability properties of functions , Princeton , NJ : Princeton Mathematical Series, No. 30. Princeton University Press .
- Stein , EM . 1993 . Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory integrals , Princeton , NJ : Princeton University Press . (With the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III)
- Grafakos , L . 2008 . Classical Fourier Analysis , Berlin : Springer .
- Cruz-Uribe , D , Diening , L and Fiorenza , A . 2009 . A new proof of the boundedness of maximal operators on variable Lebesgue spaces . Boll. Unione Mat. Ital. (9) , 2 ( 1 ) : 151 – 173 .
- Diening , L , Harjulehto , P , Hästö , P , Mizuta , Y and Shimomura , T . 2009 . Maximal functions in variable exponent spaces: Limiting cases of the exponent . Ann. Acad. Sci. Fenn. Math. , 34 : 503 – 522 .
- Malý , J and Ziemer , WP . 1997 . Fine Regularity of Solutions of Elliptic Partial Differential Equations , Providence , RI : Mathematical Surveys and Monographs. Vol. 51, American Mathematical Society .
- Lewis , JL . 1988 . Uniformly fat sets . Trans. Amer. Math. Soc. , 308 ( 1 ) : 177 – 196 .
- Adams , RA . 1975 . Sobolev Spaces , New York, London : Academic Press, A Subsidiary of Harcourt Brace Jovanovich, Publishers .
- Fan , XL and Zhao , D . 2001 . On the spaces L p(x)(Ω) and W m,p(x)(Ω) . J. Math. Anal. Appl. , 263 : 424 – 446 .