The dimension of a set of singularities of weak solutions to the Navier-Stokes equations
The grand vision of a Digital Mathematics Library (DML), coordinated by a group of institutions that establish polices and practices regarding digitization, management, access, and preservation, has not come to pass. The project encountered two related problems: it was overly ambitious, and the approach to realizing it confused local and community responsibilities. While the vision called for a network of distributed, interoperable repositories, we approached and planned the project as if we were...
By taking into account the work of J. Rataj and M. Zähle [Geom. Dedicata 57, 259-283 (1995; Zbl 0844.53050)], R. Schneider and W. Weil [Math. Nachr. 129, 67-80 (1986; Zbl 0602.52003)], W. Weil [Math. Z. 205, 531-549 (1990; Zbl 0705.52006)], an integral formula is obtained here by using the technique of rectifiable currents.This is an iterated version of the principal kinematic formula for sets of positive reach and generalized curvature measures.
The Legendre transformations on differential spaces (in the sense of Sikorski) is studied, and some properties for spaces with singularities are investigated. A mechanical interpretation of the Legendre transformation is also given.