Browsing Analysis of Partial Differential Equations (APDE) by Title
Now showing items 103-122 of 208
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The observational limit of wave packets with noisy measurements
(2019)The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ... -
On a hyperbolic system arising in liquid crystal modelling
(2017-11)We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ... -
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
Della Porta, F.; Rüland, A.; Taylor, J.M.
; Zillinger, C. (2021-07-01)
Building on the work by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv:1810.04380), Torrents et al (2017 Phys. Rev. E 95 ... -
On a sharp Poincare-type inequality on the 2-sphere and its application in micromagnetics
(2019-08-21)The main aim of this note is to prove a sharp Poincaré-type inequality for vector-valued functions on $\mathbb{S}^2$ that naturally emerges in the context of micromagnetics of spherical thin films. -
On Bloom type estimates for iterated commutators of fractional integrals
(2018-04)In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ... -
On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
Boggarapu, P.; Roncal, L.; Thangavelu, S. (2019-09)
We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ... -
On pointwise and weighted estimates for commutators of Calderón-Zygmund operators
(2017)In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... -
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(2016-09-10)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... -
On the absolute divergence of Fourier series in the infinite dimensional torus
Fernández, E.; Roncal, L. (2019-03-22)
In this note we present some simple counterexamples, based on quadratic forms in infinitely many variables, showing that the implication $f\in C^{(\infty}(\mathbb{T}^\omega)\Longrightarrow\sum_{\bar{p}\in\mathbb{Z}^\inf ... -
On the bound states of Schrödinger operators with $\delta$-interactions on conical surfaces
(2016-06-30)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$-interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... -
On the controllability of Partial Differential Equations involving non-local terms and singular potentials
(2016-12-12)In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ... -
On the energy of critical solutions of the binormal flow
Banica, V.; Vega, L. (2019-07-20)
The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen- berg model in ferromagnetism, and the 1-D cubic Schr ... -
On the energy of critical solutions of the binormal flow
Banica, V.; Vega, L. (2020-07-02)
The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic ... -
On the Evolution of the Vortex Filament Equation for regular M-polygons with nonzero torsion
De la Hoz, F.; Kumar, S.; Vega, L. (2019-09-03)
In this paper, we consider the evolution of the Vortex Filament equa- tion (VFE): Xt = Xs ∧ Xss, taking M-sided regular polygons with nonzero torsion as initial data. Us- ing algebraic techniques, backed by numerical ... -
On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
(2018-09)We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ... -
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... -
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejcirik, D.; Laptev, A.; Vega, L. (2018-07-12)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... -
On the improvement of the Hardy inequality due to singular magnetic fields
Fanelli, L.; Krejčiřík, D.; Laptev, A.; Vega, L. (2020-09-01)
We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ... -
On the influence of gravity on density-dependent incompressible periodic fluids
(2019)The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ... -
On the regularity of solutions to the k-generalized korteweg-de vries equation
Kenig, C.E.; Linares, F.; Ponce, G.; Vega, L. (2018-07)
This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...