Higher order variational problems on two-dimensional domains

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 31, Issue 1, 2006, Pages 349-362

  Bildhauer, Michael ^a   Fuchs, Martin ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649357966     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. Adams, R. A.: Sobolev spaces. - Academic Press, New York-San Francisco-London, 1975.
2. Bildhauer, M.: Convex Variational Problems: Linear, Nearly Linear and Anisotropic Growth Conditions. - Lecture Notes in Math. 1818, Springer, Berlin-Heidelberg-New York, 2003.
3. Bildhauer, M., and M. Fuchs: Higher order variational inequalities with non-standard growth conditions in dimension two: plates with obstacles. - Ann. Acad. Sci. Fenn. Math. 26, 2001, 509-518.
4. Bildhauer, M., and M. Fuchs: Two-dimensional anisotropic variational problems. -Calc. Var. 16, 2003, 177-186.
5. Bildhauer, M., and M. Fuchs: Variants of the Stokes problem: the case of anisotropic potentials. - J. Math. Fluid Mech. 5, 2003, 364-402.
6. Bildhauer, M., M. Fuchs, and X. Zhong: A lemma on the higher integrability of functions with applications to the regularity theory of two-dimensional generalized Newtonian fluids. - Manuscripta Math. 116, 2005, 135-156.
7. Chudinovich, I., and C. Constanda: Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation. - Chapman and Hall, 2000.
8. Ciarlet, P., and P. Rabier: Les équations de von Kármán. - Lecture Notes in Math. 826, Springer, Berlin-Heidelberg-New York, 1980.
9. Esposito, L., F. Leonetti, and G. Mingione: Regularity results for minimizers of irregular integrals with (p; q) -growth. - Forum Math. 14, 2002, 245-272.
10. Friedman, A.: Variational Principles and Free Boundary Problems. - Wiley-Interscience, 1982.
11. Fuchs, M., G. Li, and O. Martio: Second order obstacle problems for vectorial functions and integrands with subquadratic growth. - Ann. Acad. Sci. Fenn. Math. 23, 1998, 549-558.
12. Giaquinta, M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. - Ann. of Math. Stud. 105, Princeton University Press, Princeton 1983.
13. Giaquinta, M., and G. Modica: Regularity results for some classes of higher order non linear elliptic systems. - J. Reine Angew. Math. 311/312, 1979, 145-169.
14. Gilbarg, D., and N. Trudinger: Elliptic Partial Differential Equations of the Second Order. - Second Edition, Springer-Verlag, Berlin-Heidelberg, 1983.
15. Ladyzhenskaya, O. A., and N. N. Ural'tseva: Linear and Quasilinear Elliptic Equations. - Nauka, Moskow, 1964. English transl:: Academic Press, New York 1968.
16. Morrey, C. B.: Multiple Integrals in the Calculus of Variations. - Grundlehren Math. Wiss. 130, Springer, Berlin-Heidelberg-New York, 1966.
17. Necăs, J., and I. Hlávácek: Mathematical Theory of Elastic and Elasto-Plastic Bodies. - Elsevier, New York, 1981.
18. Zeidler, E.: Nonlinear Functional Analysis and Its Applications IV. Applications to Mathematical Physics. - Springer, Berlin-Heidelberg-New York, 1987.