Displaying similar documents to “Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional”

Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects

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            () + u ˙ () + (()) + (()) = 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...

Exact null internal controllability for the heat equation on unbounded convex domains

Viorel Barbu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The liner parabolic equation y t - 1 2 𝔻 y + F · y = 1 0 u ∂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.

Relaxation in BV of integrals with superlinear growth

Parth Soneji (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study properties of the functional loc ( u , Ω ) : = inf ( u j ) lim inf j Ω f ( u j ) x ( u j ) W loc 1 , r Ω , u j u in Ω , , F loc ( u,Ω ) : = inf ( u j ) lim inf j → ∞ ∫ Ω f ( ∇ u j ) d x , whereu ∈ BV(Ω;R N ), and f:R N × n → R is continuous and satisfies 0 ≤ f(ξ)...

Higher-order phase transitions with line-tension effect

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...

Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

Similarity:

Let 𝔽 F be a filtration andbe a random time. Let 𝔾 G be the progressive enlargement of 𝔽 F with. We study the following formula, called the optional splitting formula: For any 𝔾 G-optional process, there exists an 𝔽 F-optional process and a function defined on [0∞] × (ℝ × ) being [ 0 , ] 𝒪 ( 𝔽 ) ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y = Y ' 1 [ 0 , τ ) + Y ' ' ( τ ) 1 [ τ , ) . Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...

Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions

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, div ( μ ( u + u t ) ) + ( λ div u ) + V u = 0 where and are Lipschitz continuous and . The method is based on the Carleman estimate with polynomial weights for the Lamé operator.

Expansions for the distribution of M-estimates with applications to the Multi-Tone problem

Christopher S. Withers, Saralees Nadarajah (2011)

ESAIM: Probability and Statistics

Similarity:

We give a stochastic expansion for estimates θ ^ 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 θ ^ needed for the Edgeworth expansions for the distribution and density ) to magnitude (or to for the symmetric...

A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity

Andrew Lorent (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain  ⊂ ℝthe functional is I ( u ) = 1 2 Ω - 1 | 1 - | D u | 2 | 2 + | D 2 u | 2 d z I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z wherebelongs to the subset of functions in W 0 2 , 2 ( Ω ) W02,2(Ω) whose gradient (in the sense of trace) satisfies()·  = 1 where is the inward pointing unit normal to at . In [1...

Limit theorems for measure-valued processes of the level-exceedance type

Andriy Yurachkivsky (2011)

ESAIM: Probability and Statistics

Similarity:

Let, for each ∈ , (, ۔) be a random measure on the Borel -algebra in ℝ such that E(, ℝ) < ∞ for all and let ψ ^ (, ۔) be its characteristic function. We call the function ψ ^ ( ,…, ; ,…, ) = 𝖤 j = 1 l ψ ^ ( t j , z j ) of arguments ∈ ℕ, , … ∈ , , ∈ ℝ the of the measure-valued random function (MVRF) (۔, ۔). A general limit theorem for MVRF's in terms of covaristics is proved and...

Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations

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 d 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...

Coarse quantization for random interleaved sampling of bandlimited signals

Alexander M. Powell, Jared Tanner, Yang Wang, Özgür Yılmaz (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let be a bandlimited signal that is sampled on a collection of interleaved grids  { +  } with offsets { T n } n = 1 N [ 0 , T ] T n n = 1 N ⊂ [ 0 ,T ] . If the offsets are chosen independently and uniformly at random from  [0]  and if the sample values of are quantized with a first order Sigma-Delta algorithm, then with high probability the quantization...

Semimartingale decomposition of convex functions of continuous semimartingales by brownian perturbation

Nastasiya F. Grinberg (2013)

ESAIM: Probability and Statistics

Similarity:

In this note we prove that the local martingale part of a convex function of a -dimensional semimartingale  =  +  can be written in terms of an Itô stochastic integral ∫()d, where () is some particular measurable choice of subgradient ∇ f ( x ) of at , and is the martingale part of . This result was first proved by Bouleau in [N. Bouleau, 292 (1981) 87–90]. Here we present a new treatment of the problem. We first prove the result for X ˜ = X + ϵ B x10ff65; X = X + ϵB , > 0, where is...

A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

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 ( λ S ) x1d4ab;() and ( μ T ) 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...

Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy

Jean Brossard, Christophe Leuridan (2012)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Let be a measurable transformation of a probability space ( E , , π ) , preserving the measure. Let be a random variable with law . Call (⋅, ⋅) a regular version of the conditional law of given (). Fix B . We first prove that if is reachable from -almost every point for a Markov chain of kernel , then the -orbit of -almost every point visits . We then apply this result to the Lévy transform, which transforms the Brownian motion into the Brownian motion || − , where is the local time at 0...

Continuity of solutions of a nonlinear elliptic equation

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 a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing:ℝ → ℝ

Penalization versus Goldenshluger − Lepski strategies in warped bases regression

Gaëlle Chagny (2013)

ESAIM: Probability and Statistics

Similarity:

This paper deals with the problem of estimating a regression function , in a random design framework. We build and study two adaptive estimators based on model selection, applied with warped bases. We start with a collection of finite dimensional linear spaces, spanned by orthonormal bases. Instead of expanding directly the target function on these bases, we rather consider the expansion of  =  ∘ , where is the cumulative distribution function of the design, following...

A new H(div)-conforming p-interpolation operator in two dimensions

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() 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 𝐇 ˜ (div, ), which is closely related...

The H–1-norm of tubular neighbourhoods of curves

Yves van Gennip, Mark A. Peletier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the -norm of the function 1 on tubular neighbourhoods of curves in 2 . We take the limit of small thickness, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit → 0, containing contributions from the length of the curve (at order ), the ends ( ), and the curvature ( ). The second result is a Γ-convergence result, in which the central curve may vary along...

The structure of reachable sets for affine control systems induced by generalized Martinet sub-lorentzian metrics

Marek Grochowski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we investigate analytic affine control systems q ˙ = ,  ∈  [] , where is an orthonormal frame for a generalized Martinet sub-Lorentzian structure of order of Hamiltonian type. We construct normal forms for such systems and, among other things, we study the connection between the presence of the singular trajectory starting at on the boundary of the reachable set from with the minimal number of analytic functions needed for...

Homogenization of a Periodic Parabolic Cauchy Problem in the Sobolev Space (ℝ)

T. Suslina (2010)

Mathematical Modelling of Natural Phenomena

Similarity:

In (ℝ; ℂ), we consider a wide class of matrix elliptic second order differential operators 𝒜 with rapidly oscillating coefficients (depending on /). For a fixed > 0 and small > 0, we find approximation of the operator exponential exp(− 𝒜 ) in the ( (ℝ; ℂ) → (ℝ; ℂ))-operator norm...

Exponential deficiency of convolutions of densities

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

Similarity:

If a probability density (x) (x ∈ ℝ) is bounded and := ∫e (x)dx < ∞ for some linear functional u and all  ∈ (01), then, for each  ∈ (01) and all large enough , the -fold convolution of the -tilted density p ˜ t ˜pt := e (x)/ is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...

Some problems in automata theory which depend on the models of set theory

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 L ( 𝒜 ) (x1d49c;) accepted by a Büchi 1-counter automaton 𝒜 x1d49c;. We prove the following surprising result: there exists a 1-counter Büchi automaton 𝒜 x1d49c; such that the cardinality of the complement L ( 𝒜 ) - (𝒜) of the -language...