Lusin's condition (N) for the space mappings W 1, n under analytic assumptions
Tóm tắt
We give a sufficient analytic condition in order that a mapping f∈W
1,
n
(ωR
n) satisfies Lusin's condition (N).
Tài liệu tham khảo
L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, CRC Press (1992).
H. Federer, Geometric measure theory, Springer (New York, 1969).
M. Giaquinta, G. Modica, and J. SouČek, Cartesian currents in the calculus of variations. I, (Berlin, 1998).
D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Springer (New York, 1983).
W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press (Princeton, NJ, 1942).
N. Lusin, Integrale et série trigonométrique, (Moscow, 1915) (in Russian).
J. MalÝ, The area formula for W 1,n-mappings, Comment. Math. Univ. Carolin., 35(1994), 291-298.
J. MalÝ and O. Martio, Lusin's condition (N) and mappings of the class W 1,n, J. reine angew. Math., 458(1995), 19-36.
M. Marcus and V. J. Mizel, Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems, Bull. Amer. Math. Soc., 79(1973), 790-795.
O. Martio and W. P. Ziemer, Lusin's condition (N) and mappings with non-negative Jacobians, Michigan Math. J., 39(1992), 495-508.
S. P. Ponomarev, Property N of homeomorphisms of the class W 1,p, Siberian Math. J., 28(1987), 291-298.
T. RadÓ and P. V. Reichelderfer, Continuous transformations in analysis, Springer (New York, 1955).
Yu. G. Reshetnyak, Space mappings with bounded distortion, Transl. Math. Monographs 73, Amer. Math. Soc. (Providence, RI, 1989).
S. Rickman, Quasiregular mappings, Springer (New York, 1993).
W. P. Ziemer, Weakly differentiable functions, Graduate Texts in Mathematics 120, Springer (New York, 1989).