Regularization of convex variational problems with applications to generalized Newtonian fluids

Archiv der Mathematik

Volumn 84, Issue 2, 2005, Pages 155-170

  Bildhauer, Michael ^a   Fuchs, Martin ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17644365760     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-004-1221-x     Document Type: Article

References (19)

1. R. A. ADAMS, Sobolev spaces. New York-San Francisco-London 1975.
2. D. APUSHXINSXAYA, M. BILDHAUER and M. FUCHS, Steady states of anisotropic generalized Newtonian fluids. To appear in J. Math. Fluid Mech.
3. M. BILDHAUER, Convex variational problems: linear, nearly linear and anisotropic growth conditions. LNM 1818, Berlin-Heidelberg-New York 2003.
4. M. BILDHAUER and M. FUCHS, Variants of the Stokes problem: the case of anisotropic potentials. J. Math. Fluid Mech. 5, 364-402 (2003).
5. 1,α-estimates for (double) obstacle problems under nonstandard growth conditions. Z. Anal. Anw. 20, no. 4, 959-985 (2001).
6. M. BILDHAUER, M. FUCHS and G. SEREOIN, Local regularity of solutions of variational problems for the equilibrium configuration of an incompressible, multiphase elastic body. Nonlinear Differential Equ. Appl. 8, 53-81 (2001).
7. B. DACOROONA, Direct methods in the calculus of variations. Appl. Math. Sci. 78. Berlin-Heidelberg-New York 1989.
8. L. C. EVANS and R. GARIEPY, Measure theory and fine properties of functions. Studies Adv. Math. Boca Raton-Ann Arbor-London 1992.
9. J. FREHSE, J. MÁLEK and M. STEINHAUER, On analysis of steady flows of fluids with shear-dependent viscosity based on the Lipschitz truncation method. SIAM J. Math. Anal. 34(5), 1064-1083 (2003).
10. M. FUCHS and G. SEREGIN, Variational methods for problems from plasticity theory and for generalized Newtonian fluids. LNM 1749, Berlin-Heidelberg-New York 2000.
11. G. GALDI, An introduction to the mathematical theory of the Navier-Stokes equations, Vol. 1. Springer Tracts in Natural Philosophy 38. New York 1994.
12. G. GALDI, An introduction to the mathematical theory of the Navier-Stokes equations, Vol. 2. Springer Tracts in Natural Philosophy 39. New York 1994.
13. D. GILBARG and N. S. TRUDINGER, Elliptic partial differential equations of second order, Grundlehren Math. Wiss. 224, second ed., revised third print, Berlin-Heidelberg-New York 1998.
14. 1,α-solutions to a class of nonlinear fluids in two dimensions -stationary Dirichlet problem. Zap. Nauchn. Sem. St.-Petersburg Odtel. Math. Inst. Steklov (POMI) 259, 89-121 (1999).
15. O. A. LADYZHENSKAYA, The mathematical theory of viscous incompressible flow. New York-London-Paris 1969.
16. 1,α regularity for minimizers of integral functional with L log L growth. Z. Anal. Anw. 18, 1083-1100 (1999).
17. P. P. MOSCOLOV and V. P. MIASMKOV, On the correctness of boundary value problems in the mechanics of continuous media. Math. USSR Sb. 17, 257-268 (1972).
18. G. SEREGIN, Twodimensional variational problems in plasticity theory. Izv. Russian Academy of Sciences 60 (1996), 175-210 (in Russian). English translation: Izvestiya Mathematics 60.1, 179-216 (1996).
19. G. SEREGIN, Twodimensional variational problems in plasticity theory. Izv. Russian Academy of Sciences 60 (1996), 175-210 (in Russian). English translation: Izvestiya Mathematics 60.1, 179-216 (1996).