Search results for "Operator"
showing 10 items of 1427 documents
Fourier integral operators and inhomogeneous Gevrey classes
1988
Fourier integral operators with inhomogeneous amplitude and phase junction are studied in the frame of Gevrey classes. Applications are given to propagation of singularities for a pseudodifferential equation.
The Navier–Stokes equations in exterior Lipschitz domains: L -theory
2020
Abstract We show that the Stokes operator defined on L σ p ( Ω ) for an exterior Lipschitz domain Ω ⊂ R n ( n ≥ 3 ) admits maximal regularity provided that p satisfies | 1 / p − 1 / 2 | 1 / ( 2 n ) + e for some e > 0 . In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on L σ p ( Ω ) for such p. In addition, L p - L q -mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier–Stokes equations in the critical space L ∞ ( 0 , T ; L σ 3 ( Ω ) ) (locally in time and globally in time for small initial data).
Guía clínica en el manejo perioperatorio para la cirugía de resección pulmonar por videotoracoscopia (Sección de Anestesia Cardiaca, Vascular y Torác…
2022
Resumen La introduccion de tecnicas toracoscopicas asistidas por video en cirugia toracica (VATS) ha permitido realizar un nuevo enfoque en la cirugia toracica. El acceso videotoracoscopico se realiza con pequenas incisiones, preservando al maximo los musculos y los tejidos. En la actualidad, la VATS se considera de eleccion en la mayoria de los procedimientos toracicos, principalmente debido a la menor morbimortalidad asociada. La reseccion pulmonar por VATS presenta reduccion de las fugas de aire prolongadas, arritmias, neumonia, dolor postoperatorio y una disminucion de los marcadores inflamatorios. Esta reduccion de las complicaciones postoperatorias esta vinculada a una reduccion de la…
Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking by anomalous localized resonance II
2014
If a body of dielectric material is coated by a plasmonic structure of negative dielectric constant with nonzero loss parameter, then cloaking by anomalous localized resonance (CALR) may occur as the loss parameter tends to zero. The aim of this paper is to investigate this phenomenon in two and three dimensions when the coated structure is radial, and the core, shell and matrix are isotropic materials. In two dimensions, we show that if the real part of the permittivity of the shell is $-1$ (under the assumption that the permittivity of the background is $1$), then CALR takes place. If it is different from $-1$, then CALR does not occur. In three dimensions, we show that CALR does not occu…
Some perturbation results through localized SVEP
2016
Some classical perturbation results on Fredholm theory are proved and extended by using the stability of the localized single-valued extension property under Riesz commuting perturbations. In the last part, we give some results concerning the stability of property (gR) and property (gb.
Local regularity for quasi-linear parabolic equations in non-divergence form
2018
Abstract We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p -Laplacian type and in non-divergence form. We provide local Holder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Holder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.
Nonlinear nonhomogeneous Neumann eigenvalue problems
2015
We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.
A class of weak pseudo-bosons and their bi-coherent states
2022
In this paper we extend some previous results on weak pseudo-bosons and on their related bi-coherent states. The role of {\em compatible} functions is discussed in details, and some examples are considered. The pseudo-bosonic ladder operators analysed in this paper generalize significantly those considered so far, and a class of new diagonalizable manifestly non self-adjoint Hamiltonians are deduced.
Singular integrals on regular curves in the Heisenberg group
2019
Let $\mathbb{H}$ be the first Heisenberg group, and let $k \in C^{\infty}(\mathbb{H} \, \setminus \, \{0\})$ be a kernel which is either odd or horizontally odd, and satisfies $$|\nabla_{\mathbb{H}}^{n}k(p)| \leq C_{n}\|p\|^{-1 - n}, \qquad p \in \mathbb{H} \, \setminus \, \{0\}, \, n \geq 0.$$ The simplest examples include certain Riesz-type kernels first considered by Chousionis and Mattila, and the horizontally odd kernel $k(p) = \nabla_{\mathbb{H}} \log \|p\|$. We prove that convolution with $k$, as above, yields an $L^{2}$-bounded operator on regular curves in $\mathbb{H}$. This extends a theorem of G. David to the Heisenberg group. As a corollary of our main result, we infer that all …
Sampling methods for low-frequency electromagnetic imaging
2007
For the detection of hidden objects by low-frequency electromagnetic imaging the linear sampling method works remarkably well despite the fact that the rigorous mathematical justification is still incomplete. In this work, we give an explanation for this good performance by showing that in the low-frequency limit the measurement operator fulfils the assumptions for the fully justified variant of the linear sampling method, the so-called factorization method. We also show how the method has to be modified in the physically relevant case of electromagnetic imaging with divergence-free currents. We present numerical results to illustrate our findings, and to show that similar performance can b…