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Abstract The concept of curve of maximal slope, a generalized notion of gradient flow, is extended to the setting of length spaces, which includes all metric spaces. This extended definition is used to show that curves of maximal slope in a metric space do not depend on the full metric, but only...
Abstract We construct an example of a Steiner tree with an infinite number of branching points connecting an uncountable set of points. Such a tree is proven to be the unique solution to a Steiner problem for the given set of points. As a byproduct we get the whole family of explicitly defined...
Abstract We prove that, given a planar bi-Lipschitz map u defined on the boundary of the unit square, it is possible to extend it to a function v of the whole square, in such a way that v is still bi-Lipschitz. In particular, denoting by L and L ˜ the bi-Lipschitz constants of u and v , with our...
Abstract We consider a semilinear Robin problem driven by the Laplacian with a reaction which does not satisfy a global growth condition, only a local one. Using variational methods coupled with truncation and perturbation techniques and Morse theory, we prove two multiplicity theorems producing...
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