796 research outputs found
Existence Results for Minimizers of Parametric Elliptic Functionals
No full textWe prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem
Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case
No full textIn this paper we use the new regularity and stability estimates for Alexandrov solutions to Monge-Ampere equations estabilished by G.De Philippis and A.Figalli to provide a global in time existence of distributional solutions to a semigeostrophic equation on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed
The use of exopolysaccharide-producing cyanobacteria as biosorbents to remove copper from industrial wastewaters
No full textThe accumulation of heavy metals in water bodies represent a widespread cause of pollution, and poses the need
to develop novel technologies to remove metals at the source, abating the costs of the commonly used chemical
and physio-chemical methods. The use of cyanobacteria as biosorbents has been acknowledged as a promising
alternative, due to their charged polysaccharidic envelopes which have affinity for metal ions. Nonetheless, the
reseach must move towards: i) assessing the effectiveness of the process towards complex wastewater solutions
which contain chemical species that can interfere with the sorption process, also considering the characteristics
of the used strains, and ii) developing novel devices that support biomass growth and use, in order to achieve
a scaling up of the process. We compared the specific removal of three cyanobacteria, Cyanothece 16 Som 2,
Cyanothece ET5 and Cyanospira capsulata, towards Cu2+ contained, with various other metals, in two industrial
effluents (one at pH 1.26 and one at pH 10.26). The strains were selected due to their previously assayed affinity
toward Cu2+ in pure solutions (De Philippis et al. 2011). Acid or basic pretreatments (respectively for the acid
and the basic effluent) were performed in the tentative to increase the specific removal. Metal concentration in
solution, before and after the contact with the biomasses, was determined by atomic absorption spectrometry.
Specific removals resulted different to those obtained towards pure metal solutions, likely due to the presence of
other competing ions. Cyanothece 16 Som 2 showed the highest Cu2+ specific removal towards both the effluents.
The pretreatment was effective only in the case of the basic effluent. Results proved the capacity of Cyanothece 16
Som 2 to act as a selective Cu2+ sorbent even in the presence of complex solutions. A novel prototype device is
being projected in order to support the growth and the immobilization of the cyanobacterial biomass for its use in
industrial field.
De Philippis et al. 2011. Applied Microbiology and Biotechnology 92, 697-708
Non-collapsed spaces with Ricci curvature bounded from below
No full text— We propose a definition of non-collapsed space with Ricci curvature bounded from below and we prove the versions of Colding’s volume convergence theorem and of Cheeger-Colding dimension gap estimate for RCD spaces. In particular this establishes the stability of non-collapsed spaces under non-collapsed Gromov-Hausdorff convergence
Surviving without monotonicity: anisotropic Michael-Simon inequality
No full textThe monotonicity formula for the area functional (and for other important functionals enjoying enough symmetry, such as the Dirichlet energy for maps, the Yang-Mills energy for connections, etc) is a basic tool used crucially in the proof of a number of fundamental facts, including the upper semicontinuity of the support for a sequence of stationary varifolds (with a lower density bound), the compactness of stationary rectifiable varifolds and the existence of tangent cones. The first two are particularly mportant in soft arguments by compactness and contradiction.
Here we discuss the anisotropic version of the Michael-Simon inequality, which we can prove for (strictly) convex anisotropic integrands for two-dimensional varifolds in R^3, provided that the integrand is close to the area in the C^1 topology. This inequality, which we conjecture to hold even without the closeness constraint, is good enough to obtain lower area bounds when the density of the varifold is bounded below. This allows to recover upper semicontinuity of the support, compactness of rectifiable and integral varifolds, and it also allows to prove Allard's regularity theorem in this setting (using also recent work by De Rosa-Tione), where the monotonicity formula is probably false.
The proof is deeply inspired by posthumous notes by Almgren, devoted to the same result. Although our arguments overlap with Almgren's, some parts are greatly simplified and rely on a nonlinear inequality bounding the L^1-norm of the determinant of a function, from the plane to 2x2 matrices, with the L^1-norms of the divergence of the rows, provided the matrix obeys (pointwise) some nonlinear constraints. This inequality can be seen as a version of the multilinear Kakeya inequality on the plane. This is joint work with Guido De Philippis (NYU)
Weak notions of jacobian determinant and relaxation
No full textIn this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals
Hydrogen Production and Possible Impact on Global Energy Demand: Open Problems and Perspectives
No full textThe main goal of this Chapter is to take the reader to the unconventional concept that if
hydrogen is used as an energy carrier, there are consistent benefi ts to be expected, depending
on how hydrogen is generated. As it will be illustrated, the technical problems lying ahead of
the creation of an apparent “Hydrogen Based Society” are of technical nature although we
are all confi dent that they can be solved within a reasonable period of time
Higher Integrability for Minimizers of the Mumford-Shah Functional
No full textWe prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi (Free discontinuity problems in calculus of variations. Frontiers in pure and applied mathematics, North-Holland, Amsterdam, pp 55-62, 1991). © 2014 Springer-Verlag Berlin Heidelberg
Obituary: Prof. A. de Philippis
No full textOn the 6th of April 2002 prof. Alessandro De Philippis passed away in Firenze. Born in 1908 he graduated in Agriculture in 1930 and in 1931 was appointed Researcher at the Research Station for Silviculture in Firenze where he was active until 1942. In the same year he became Professor of Forest Ecology and Silviculture at the University of Firenze where he taught until 1979. The Accademia Italiana di Scienze Forestali elected him as President in 1980 and he hold the post until 1992. De Philippis developed research mainly on forestry problems of the Mediterranean area: ecology of spontaneous and exotic (especially Eucalipts) tree species, climate, planting methods. His large scientific production deals with silvicultural systems, plantations, ecology, genetics, conservation, wood production, has been since the beginning clearly aimed at giving support to the implementation of a silviculture ecologically oriented in the Mediterranean area. He gave a precious conceptual contribution to clarify the connections between forestry and environmental problems and therefore the position of silviculture in the modern multiple use forestry
Regularity of optimal transport maps and applications
No full textIn this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier’ theorem on existence of optimal transport maps and of Caffarelli’s Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero
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