L2 well-posedness of planar div-curl systems

Archive for Rational Mechanics and Analysis

Volumn 160, Issue 2, 2001, Pages 91-134

  Auchmuty, Giles ^a   Alexander, James C ^b  

^a University of Houston   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035621389     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050100156     Document Type: Article

References (18)

1. R. ABRAHAM, J. E. MARSDEN & T. RATIU, Manifolds, Tensor Analysis and Applications, 2nd. ed., Springer Verlag, New York (1988).
2. C.J. AMICK, Some remarks on Rellich's theorem and the Poincaré inequality. J. London Math. Soc. (2) 18 (1973), 81-93.
3. G. AUCHMUTY, Orthogonal decompositions and bases for three-dimensional vector fields. Numer. Funct. Anal. and Optimiz. 15 (1994), 445-488.
4. G. AUCHMUTY, Reconstruction of the velocity from the vorticity in three-dimensional fluid flows. Proc. Royal Soc. Lond. A 454 (1998), 607-630.
5. P. BAMBERG & S. STERNBERG, A Course in Mathematics for Students of Physics, volume 2, Cambridge Univ. Press (1990).
6. P. BLANCHARD & E. BRÜNING, Variational Methods in Mathematical Physics, Springer Verlag, Berlin (1992).
7. J. BOLIK & W. VON WAHL, Estimating ∇u in terms of div u, curl u and either u · ν or u × ν and the topology. Math. Methods in the Applied Sciences 20 (1997), 737-744.
8. R. DAUTRAY & J. L. LIONS (eds.), Mathematical Analysis and Numerical Methods for Science and Technology. 6 volumes, Springer Verlag, Berlin (1990).
9. L. C. EVANS & R. F. GARIEPY, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton (1992).
10. P. FERNANDES & G. GILARDI, Magnetostatic and electrostatic problems in inhomogeneous anisotropic media with irregular boundary and mixed boundary conditions. Math. Models and Methods in Applied Sciences 7 (1997), 957-991.
11. L. E. FRAENKEL, On the regularity of the boundary in the theory of Sobolev spaces. Proc. London Math. Soc. (3), 39 (1979), 385-427.
12. V. GIRAULT & P. A. RAVIART, Finite Element Methods for the Navier-Stokes Equations, Springer Verlag, Berlin (1986).
13. R. PICARD, On the boundary value problems of electro-and magnetostatics. Proc. Royal Society of Edinburgh, 92 A (1982), 165-174.
14. J. SARANEN, On generalized harmonic fields in domains with anisotropic non-homogeneous media. J. Math. Anal. Appl. 88 (1982), 104-115.
15. J. SARANEN, On an inequality of Friedrichs. Math. Scand. 51 (1982), 310-322.
16. H. WEYL, The method of orthogonal projection in potential theory. Duke Math. J. 7 (1940), 411-444.
17. J. WLOKA, Partial Differential Equations. Cambridge University Press, (1987).
18. E. ZEIDLER, Nonlinear Functional Analysis and its Applications, III: Variational Methods and Optimization. Springer Verlag, New York (1985).