1,721,278 research outputs found
ASYMPTOTIC ANALYSIS OF AMBROSIO-TORTORELLI ENERGIES IN LINEARIZED ELASTICITY
No full textWe provide an approximation result in the sense of Gamma-convergence for energies of the form integral(Omega) L-1 (e(u)) dx + a Hn-1 (J(u)) + b integral (Ju) L-0(1/2) ([u] circle dot nu(u)) dH(n-1) where Omega subset of R-n is a bounded open set with Lipschitz boundary, L-0 and L-1 are coercive quadratic forms on M-sym(nxn), a, b are positive constants, and u runs in the space of fields SBD2(Omega); i.e., it's a special field with bounded deformation such that its symmetric gradient e(u) is square integrable, and its jump set J(u) has finite (n-1)-Hausdorff measure in R-n. The approximation is performed by means of Ambrosio-Tortorellitype elliptic regularizations, the prototype example being integral(Omega) (v vertical bar e(u)vertical bar(2) + gamma epsilon vertical bar del v vertical bar(2)) dx, where (u, v) is an element of H-1(Omega, R-n) x H-1(Omega), epsilon <= v <= 1, and gamma > 0
The local structure of the free boundary in the fractional obstacle problem
No full textBuilding upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125-184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in Rn+1 with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null Hn-1 measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125-184] and therefore we retrieve the same results: Local finiteness of the (n-1)-dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure), Hn-1-rectifiability of the free boundary, classification of the frequencies and of the blowups up to a set of Hausdorff dimension at most (n-2) in the free boundary. Instead, if φ ∈ Ck+1(Rn), k ≥ 2, similar results hold only for distinguished subsets of points in the free boundary where the order of contact of the solution with the obstacle function φ is less than k + 1
Trimetazidine:an innovative approach to ischemic heart disease in different subsets of patients
No full textRelaxation of free-discontinuity energies with obstacles,
No full textGiven a Borel function ψ defined on a bounded open set Ω with Lipschitz boundary
and φ ∈ L1 (∂Ω, Hn−1 ), we prove an explicit representation formula for the L1 lower semicontinuous
envelope of Mumford-Shah type functionals with the obstacle constraint u+ ≥ ψ H^{n−1} a.e. on Ω and
the Dirichlet boundary condition u = φ on ∂Ω
Approximation by difference schemes of fracture energies: the vectorial case
No full textWe provide a variational approximation, in the sense of De
Giorgi’s Γ-convergence, by finite-difference schemes of functionals of the type
g(u+ − u− , νu ) dH2
ψ(∇u) dx +
Ω
Ju
defined for u ∈ SBV (Ω; RN ), where Ω is an open set in R3 , ψ and g are
assigned. More precisely, ψ is a quasi-convex function with p-growth, p > 1,
and g satisfies standard lower semicontinuity conditions. The approximating
functionals are of the form
ψε (∇u(x)) dx
Tε ∩Ω
where ψε is an interaction potential taking into account a separation of scales,
Tε is a suitable regular triangulation of R3 and u is affine on each element of
the assigned triangulation
Asymptotic analysis of Mumford-Shah type energies in periodically-perforated domains
No full textWe study the asymptotic limit of obstacle problems for Mumford–Shah type functionals with p-
growth in periodically perforated domains via the Γ -convergence of the associated free-discontinuity
energies. In the limit a non-trivial penalization term related to the 1-capacity of the reference hole
appears if and only if the size of the perforation scales like εn/(n−1) , ε being its periodicity. We
give two different formulations of the obstacle problem to include also perforations with Lebesgue
measure zero
How a minimal surface leaves a thin obstacle
Full text linkWe prove the optimal regularity and a detailed analysis of the free boundary of the solutions to the thin obstacle problem for nonparametric minimal surfaces with flat obstacles
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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