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Journals and Conferences
We consider Plateau type variational problems related to the size minimization of recti able currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with 0 < q 1.… (More)
This paper presents a constructive approach to estimating the size of a neural network necessary to solve a given classification problem. The results are derived using an information entropy approach in the context of limited precision integer weights. Such weights are particularly suited for hardware implementations since the area they occupy is limited,… (More)
Let f : U Ď R m Ñ Q Q p 2 q be of Sobolev class W 1,p , 1 ă p ă 8. If f almost minimizes its p Dirichlet energy then f is Hölder continuous. If p " 2 and f is squeeze and squash stationary then f is in VMO.
In this note we describe the notion of a rectifiable scan and consider some applications [DH1], [DH2] to Plateau-type minimization problems. “Scans” were first introduced in the work [HR1] of Tristan Rivière and the second author to adequately describe certain bubbling phenomena. There, the behavior of certain W 1,3 weakly convergent sequences of smooth… (More)
We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show C regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.
We give an example, in the infinite dimensional separable Hilbert space, of a purely unrectifiable Borel set with finite nonzero one dimensional Hausdorff measure, whose projection is nonnegligible in a set of directions which is not Aronszajn null. 2010 Mathematics Subject Classification: 28A75, 28A80, 53C65.
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector fields that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is finite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions. In the context of… (More)