Optimal error estimates for semidiscrete phase relaxation models
Optimal error Estimates for the Stokes and Navier–Stokes equations with slip–boundary condition
We consider a finite element discretization by the Taylor–Hood element for the stationary Stokes and Navier–Stokes equations with slip boundary condition. The slip boundary condition is enforced pointwise for nodal values of the velocity in boundary nodes. We prove optimal error estimates in the H1 and L2 norms for the velocity and pressure respectively.
Optimal error estimation for Petrov-Galerkin methods in two dimensions.
Optimal feedback control of a class of distributed-parameter systems with incomplete measurement
Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion
Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient...
Optimal feedback for perturbed bilinear control problems
Optimal grids for anisotropic problems.
Optimal interface error estimates for the mean curvature flow
Optimal interior partial regularity for nonlinear elliptic systems for the case under natural growth condition.
Optimal internal dissipation of a damped wave equation using a topological approach
We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection...
Optimal -properties of Green’s functions for non-divergence elliptic equations in two dimensions
A sharp integrability result for non-negative adjoint solutions to planar non-divergence elliptic equations is proved. A uniform estimate is also given for the Green's function.
Optimal L...-Error Estimates for Nonconforming and Mixed Finite Element Methods of Lowest Order.
Optimal L...-Error Estimates for Piecewise Linear Finite Elements in Irn for 1...n...3.
Optimal Lipschitz and LP Regularity for the Equation ...u = f on Strongly Pseudo-Convex Domains.
Optimal Lipschitz estimates for the equation on a class of convex domains
Optimal Lp estimates for the ...-equation on complex ellipsoids in Cn.
Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential...
Optimal Lyapunov inequalities and applications to nonlinear problems
Optimal measures for the fundamental gap of Schrödinger operators
We study the potential which minimizes the fundamental gap of the Schrödinger operator under the total mass constraint. We consider the relaxed potential and prove a regularity result for the optimal one, we also give a description of it. A consequence of this result is the existence of an optimal potential under L1 constraints.
Optimal multiphase transportation with prescribed momentum
A multiphase generalization of the Monge–Kantorovich optimal transportation problem is addressed. Existence of optimal solutions is established. The optimality equations are related to classical Electrodynamics.