One-sided Mullins-Sekerka flow does not preserve convexity.
Opérateurs différentiels d'ordre infini dans des espaces de fonctions entières
Opérateurs pseudo-différentiels définis en un point
We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.
Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single...
Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction ( cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known...
Optimal control approach in inverse radiative transfer problems : the problem on boundary function
Optimal control approach in inverse radiative transfer problems: the problem on boundary function
The paper presents some results related to the optimal control approachs applying to inverse radiative transfer problems, to the theory of reflection operators, to the solvability of the inverse problems on boundary function and to algorithms for solution of these problems.
Optimal control for coupled systems governed by Petrowsky type equations with control-constrained and infinite number of variables
Optimal control of a system governed by Petrowsky type equation with an infinite number of variables
Optimal control of dynamical processes in two-phase systems of solid-liquid type
Optimal control of non-well-posed distributed systems
Optimal control of the Primitive Equations of the ocean with Lagrangian observations
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
Optimal control problem and maximum principle for fractional order cooperative systems
In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...
Optimal regularity for the pseudo infinity Laplacian
In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.
Optimal regularity of lower dimensional obstacle problems.
Optimal regularization method for ill-posed Cauchy problems.
Optimal stability for inverse elliptic boundary value problems with unknown boundaries
Optimisation de forme et problème à frontière libre : cas du p-laplacien
Optimization of measurements for state estimation in parabolic distributed systems
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