8,827 research outputs found
An Epiperimetric Inequality for the Thin Obstacle problem
We prove an epiperimetric inequality for the thin obstacle problem, extending
the pioneering results by Weiss on the classical obstacle problem (Invent.
Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study
the rate of converge of the rescaled solutions to their limits, as well as the
regularity properties of the free boundary
On the measure and the structure of the free boundary of the lower dimensional obstacle problem
We provide a thorough description of the free boundary for the lower
dimensional obstacle problem in up to sets of null
measure. In particular, we prove (i) local finiteness of
the -dimensional Hausdorff measure of the free boundary, (ii)
-rectifiability of the free boundary, (iii) classification
of the frequencies up to a set of dimension at most (n-2) and classification of
the blow-ups at almost every free boundary point
Single Star-forming galaxies and Star-forming galaxies in SF+SF and mixed pairs
We compare the SFR of single star-forming galaxies with the SFR of
star-forming galaxies in pairs. Volume-limited samples are compared selected
from the 2dFGRS, applying a maximum magnitude difference criterion. We show
that SF galaxies in SF + SF pairs typically increase their SFR as they get
fainter, whereas this does not happen for SF galaxies in mixed (SF + passive)
pairs. And we provide evidence that differences between single SF and SF in
pairs get more significant when SF galaxies in mixed pairs are excluded from
the pair sample. Our analysis confirms that enhanced SFR and the presence of a
companion galaxy (on 0.5 h^-1 Mpc scale) are correlated quantities, provided
the galaxy is neither too luminous nor too faint, and the triggering galaxy is
itself a SF galaxy.Comment: 6 pages, 3 figures, contributed paper, to be published in ''The
Evolution of Starbursts'' (Bad Honnef 2004), ed. S. Huettemeister & E.
Manthley (Melville:AIP
Phase field approximation of cohesive fracture models
We obtain a cohesive fracture model as a -limit of scalar damage
models in which the elastic coefficient is computed from the damage variable
through a function of the form , with diverging for close to the value describing undamaged
material. The resulting fracture energy can be determined by solving a
one-dimensional vectorial optimal profile problem. It is linear in the opening
at small values of and has a finite limit as . If the
function is allowed to depend on the index , for specific choices we
recover in the limit Dugdale's and Griffith's fracture models, and models with
surface energy density having a power-law growth at small openings
Existence of minimizers for the d stationary Griffith fracture model
We consider the variational formulation of the Griffith fracture model in two
spatial dimensions and prove existence of strong minimizers, that is
deformation fields which are continuously differentiable outside a closed jump
set and which minimize the relevant energy. To this aim, we show that
minimizers of the weak formulation of the problem, set in the function space
and for which existence is well-known, are actually strong minimizers
following the approach developed by De Giorgi, Carriero, and Leaci in the
corresponding scalar setting of the Mumford-Shah problem
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