In this paper, we consider the elliptic system

Abstract Given a pointed metric space M , we study when there exist n -dimensional linear subspaces of $$\mathrm {Lip}_0(M)$$ Lip 0 ( M ) consisting strongly norm-attaining Lipschitz functionals, ...

Perlmutter (1970) argued that the indefinite article is categorically different from the definite article and proposed that it is a clitic version of the numeral "one". But there are, as Perlmutter himself pointed out, instances of "a" as well as of "one" that don't seem to have the semantics of the numeral. Hence a divorce of "a" (and of "one") from "numeral"-hood is called for. Furthermore, t...

Perlmutter (1970) argued that the indefinite article is categorically different from the definite article and proposed that it is a clitic version of the numeral "one". But there are, as Perlmutter himself pointed out, instances of "a" as well as of "one" that don't seem to have the semantics of the numeral. Hence a divorce of "a" (and of "one") from "numeral"-hood is called for. Furthermore, t...

The adaptive cross approximation method generates low-rank approximations to suitablem×n sub-blocks of discrete integral formulations of elliptic boundary value problems. A characteristic property is that the approximation, which requires k(m+n), k ∼ | log ε|∗, units of storage, is generated in an adaptive and purely algebraic manner using only few of the matrix entries. In this article we pres...

We are concerned with super-Liouville equations on the two sphere, which have variational structure a strongly-indefinite functional. prove existence of non-trivial solutions by combining use Nehari manifolds, balancing conditions and bifurcation theory.

We prove that key functionals (such as the volume and the number of vertices) of a random polytope is strongly concentrated, using a martingale method. As applications, we derive new estimates for high moments and the speed of convergence of these functionals.