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 these v... 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.
The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 2Revista Matematica Iberoamericana - Tập 1 Số 2 - Trang 45-121 - 1985
Pierre-Louis Lions
This paper is the second part of a work devoted to the study of variational
problems (with constraints) in functional spaces defined on domains presenting
some (local) form of invariance by a non-compact group of transformations like
the dilations in \mathbb R^N . This contains for example the class of problems
associated with the determination of extremal functions in inequalities like
Sovolev in... hiện toàn bộ