Parth Soneji (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We study properties of the functional
F loc ( u,Ω ) : = inf ( u j ) lim inf j → ∞ ∫ Ω f ( ∇ u j ) d x , where
Luca Mugnai (2013)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We establish some new results about the -limit, with respect to the -topology, of two different (but related) phase-field approximations ℰ ε ε , x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize the-limit as → 0 of ℰ, and show that in general the -limits of ℰand x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of the-limit...
Shiqi Song (2014)
ESAIM: Probability and Statistics
Similarity:
Let F be a filtration andbe a random time. Let G be the progressive enlargement of F with. We study the following formula, called the optional splitting formula: For any G-optional process, there exists an F-optional process and a function defined on [0∞] × (ℝ × ) being ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...
Viorel Barbu (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝ with smooth boundary is exactly null controllable on each finite interval if 𝒪is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here, : ℝ → ℝ is a bounded, -continuous function, and = ∇, where is convex and coercive.
Hedy Attouch, Paul-Émile Maingé (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time goes to infinity, of trajectories of second-order evolution equations () + () + (()) + (()) = 0, where is the gradient operator of a convex differentiable potential function : ,: is a maximal monotone operator which is assumed to be-cocoercive, and > 0 is a damping parameter. Potential and non-potential effects are associated...
Olivier Finkel (2011)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Similarity:
We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an -language (x1d49c;) accepted by a Büchi 1-counter automaton x1d49c;. We prove the following surprising result: there exists a 1-counter Büchi automaton x1d49c; such that the cardinality of the complement (𝒜) of the -language...
Bernardo Galvão-Sousa (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [ 4 (1987) 487–512], and in a different form by Alberti in [ is a scalar density function and and are double-well potentials, the exact scaling...
Alexei Bespalov, Norbert Heuer (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
In this paper we construct a new H(div)-conforming projection-based -interpolation operator that assumes only H() (div, )-regularity ( > 0) on the reference element (either triangle or square) . We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space (div, ), which is closely related...
Christopher S. Withers, Saralees Nadarajah (2011)
ESAIM: Probability and Statistics
Similarity:
We give a stochastic expansion for estimates that minimise the arithmetic mean of (typically independent) random functions of a known parameter. Examples include least squares estimates, maximum likelihood estimates and more generally -estimates. This is used to obtain leading cumulant coefficients of needed for the Edgeworth expansions for the distribution and density ) to magnitude (or to for the symmetric...
Hang Yu (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients , in three dimensions, where and are Lipschitz continuous and . The method is based on the Carleman estimate with polynomial weights for the Lamé operator.
T. Suslina (2010)
Mathematical Modelling of Natural Phenomena
Similarity:
In (ℝ; ℂ), we consider a wide class of matrix elliptic second order differential operators with rapidly oscillating coefficients (depending on /). For a fixed > 0 and small > 0, we find approximation of the operator exponential exp(− ) in the ( (ℝ; ℂ) → (ℝ; ℂ))-operator norm...
Pierre Étoré, Miguel Martinez (2014)
ESAIM: Probability and Statistics
Similarity:
In this note we propose an exact simulation algorithm for the solution of (1)
d X t = d W t + b̅ ( X t ) d t, X 0 = x, where
Antoine Gloria (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Similarity:
We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the -dimensional lattice with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector...
Pierre Bousquet (2013)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We consider a nonlinear elliptic equation of the form div [(∇)] + [] = 0 on a domain Ω, subject to a Dirichlet boundary condition tr = . We do not assume that the higher order term satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and satisfies a one-sided bounded slope condition, or when is radial: a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing:ℝ → ℝ
Stéphane Laurent, Catherine Legrand (2012)
ESAIM: Probability and Statistics
Similarity:
In many applications, we assume that two random observations and are generated according to independent Poisson distributions x1d4ab;() and x1d4ab;() and we are interested in performing statistical inference on the ratio = / of the two incidence rates. In vaccine efficacy trials, and are typically the numbers of cases in the vaccine and the control groups respectively, is called the relative risk and the statistical model is called ‘partial immunity model’. In this paper we...
Eva Löcherbach, Dasha Loukianova (2013)
ESAIM: Probability and Statistics
Similarity:
Consider a strong Markov process in continuous time, taking values in some Polish state space. Recently, Douc