Search results for "Bounded function"
showing 10 items of 508 documents
Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem
2016
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we prove some estimates on the rate of convergence to the exact solution.
Optimal Bounds on Plastic Deformations for Bodies Constituted of Temperature-Dependent Elastic Hardening Material
1997
Bounds are investigated on the plastic deformations in a continuous solid body produced during the transient phase by cyclic loading not exceeding the shakedown limit. The constitutive model employs internal variables to describe temperature-dependent elastic-plastic material response with hardening. A deformation bounding theorem is proved. Bounds turn out to depend on some fictitious self-stresses and mechanical internal variables evaluated in the whole structure. An optimization problem, aimed to make the bound most stringent, is formulated. The Euler-Lagrange equations related to this last problem are deduced and they show that the relevant optimal bound has a local character, i.e., it …
Quasi-linear diffusion equations with gradient terms and L1 data
2004
Abstract In this article we study the following quasi-linear parabolic problem: u t − Δ u+|u| β−2 u| ∇ u| q =|u| α−2 u| ∇ u| p in Ω×]0,T[, u(x,t)=0 on ∂Ω×]0,T[, u(x,0)=u 0 (x) in Ω, where Ω is a bounded open set of R N and T>0. We prove that if α,β>1, 0⩽p u 0 ∈L 1 (Ω) .
Singular integrals, analytic capacity and rectifiability
1997
In this survey we study some interplay between classical complex analysis (removable sets for bounded analytic functions), harmonic analysis (singular integrals), and geometric measure theory (rectifiability).
Finite speed of propagation in porous media by mass transportation methods
2004
Abstract In this Note we make use of mass transportation techniques to give a simple proof of the finite speed of propagation of the solution to the one-dimensional porous medium equation. The result follows by showing that the difference of support of any two solutions corresponding to different compactly supported initial data is a bounded in time function of a suitable Monge–Kantorovich related metric. To cite this article: J.A. Carrillo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).
Partial isometries and the conjecture of C.K. Fong and S.K. Tsui
2016
Abstract We investigate some bounded linear operators T on a Hilbert space which satisfy the condition | T | ≤ | Re T | . We describe the maximum invariant subspace for a contraction T on which T is a partial isometry to obtain that, in certain cases, the above condition ensures that T is self-adjoint. In other words we show that the Fong–Tsui conjecture holds for partial isometries, contractive quasi-isometries, or 2-quasi-isometries, and Brownian isometries of positive covariance, or even for a more general class of operators.
Transportation-cost inequality on path spaces with uniform distance
2008
Abstract Let M be a complete Riemannian manifold and μ the distribution of the diffusion process generated by 1 2 ( Δ + Z ) where Z is a C 1 -vector field. When Ric − ∇ Z is bounded below and Z has, for instance, linear growth, the transportation-cost inequality with respect to the uniform distance is established for μ on the path space over M . A simple example is given to show the optimality of the condition.
A Birkhoff type integral and the Bourgain property in a locally convex space
2007
An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.
On Spaces of Bochner and Pettis Integrable Functions and Their Set-Valued Counterparts
2011
The aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem.
Structure and stability of traversable thin-shell wormholes in Palatini f(R) gravity
2020
We study the structure and stability of traversable wormholes built as (spherically symmetric) thin shells in the context of Palatini f(R) gravity. Using a suitable junction formalism for these theories we find that the effective number of degrees of freedom on the shell is reduced to a single one, which fixes the equation of state to be that of massless stress-energy fields, contrary to the general relativistic and metric f(R) cases. Another major difference is that the surface energy density threading the thin shell, needed in order to sustain the wormhole, can take any sign and may even vanish, depending on the desired features of the corresponding solutions. We illustrate our results by…