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The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed convex...
A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.
In this paper we deal with the local exact controllability of the
Navier-Stokes system with nonlinear Navier-slip boundary
conditions and distributed controls supported in small sets. In a
first step, we prove a Carleman inequality for the linearized
Navier-Stokes system, which leads to null controllability of this
system at any time T>0. Then, fixed point arguments lead to the
deduction of a local result concerning the exact controllability
to the trajectories of the Navier-Stokes system.
The object of this paper is to prove existence and regularity results for non-linear elliptic differential-functional equations of the form over the functions that assume given boundary values ϕ on ∂Ω. The vector field satisfies an ellipticity condition and for a fixed x, F[u](x) denotes a non-linear functional of u. In considering the same problem, Hartman and Stampacchia [Acta Math.115 (1966) 271–310] have obtained existence results in the space of uniformly Lipschitz continuous functions...
On a closed convex set in with sufficiently smooth () boundary, the stop operator is locally Lipschitz continuous from into . The smoothness of the boundary is essential: A counterexample shows that -smoothness is not sufficient.
We study variational problems with volume constraints, i.e., with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a Γ-limit argument and illustrate this with numerical computations. Finally...
This paper gives a rigorous derivation
of a functional proposed by Aftalion and Rivière [Phys. Rev. A64 (2001) 043611]
to characterize the energy of vortex filaments
in a rotationally forced Bose-Einstein condensate. This
functional is derived as a Γ-limit
of scaled versions of the Gross-Pitaevsky
functional for the wave function of such a condensate. In most situations,
the vortex filament energy functional is either unbounded below
or has only trivial minimizers, but
we establish the existence...
We give a sufficient condition for a curve to ensure that the -dimensional Hausdorff measure restricted to is locally monotone.
We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve , , is locally 1-monotone.
We prove that any Kantorovich potential for the cost function c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex in the “region of interest”, without any compactness assumption on M, nor any assumption on its curvature. Such a region of interest is of full μ-measure as soon as the starting measure μ does not charge n – 1-dimensional rectifiable sets.
We prove that any Kantorovich potential for the cost function
c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex
in the “region of interest”, without any compactness assumption
on M, nor any assumption on its curvature. Such a region of
interest is of full μ-measure as soon as the starting measure
μ does not charge n – 1-dimensional rectifiable sets.
In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane....
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