Newtonian spaces: An extension of Sobolev spaces to metric measure spacesRevista Matematica Iberoamericana - Tập 16 Số 2 - Trang 243-279 - 2000
Nageswari Shanmugalingam
This paper studies a possible definition of Sobolev spaces in abstract metric spaces and answers in the affirmative the question whether this definition yields a Banach space. The paper also explores the relationship between this definition and the Hajlasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven. Different versions of capacities are also explored and...... hiện toàn bộ
Connectivity by geodesics on globally hyperbolic spacetimes with a lightlike Killing vector fieldRevista Matematica Iberoamericana - Tập 33 Số 1 - Trang 1-28 - 2017
Rossella Bartolo, Anna María Candela, José Luis Flores Dorado
Taking a globally hyperbolic spacetime endowed with a complete lightlike Killing vector field and a complete Cauchy hypersurface, we characterize the points which can be connected by geodesics. A straightforward consequence is the geodesic connectedness of globally hyperbolic generalized plane waves with a complete Cauchy hypersurface.