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18 results on '"VENKOV, GEORGE"'

1. Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions

Author

Tarulli, Mirko and Venkov, George

Subjects
Mathematics - Analysis of PDEs, 35J10, 35Q55, 35G50, 35P25
Abstract

We prove the decay in the energy space for the solution to the defocusing biharmonic Hartree-Fock equations with mass-supercritical and energy-subcritical Choquard-type nonlinearity in space dimension $d\geq3$. We treat both the free and the perturbed by a potential case. As a direct consequence, we obtain large-data scattering in $H^2(\mathbb R^d)^N, \, N\geq 1$.

Published
2021

2. Orbital stability of solitary waves for the generalized Choquard model

Author

Georgiev, Vladimir, Tarulli, Mirko, and Venkov, George

Subjects
Mathematics - Analysis of PDEs, 37K40, 35Q55, 35Q51
Abstract

We consider the generalized Choquard equation describing trapped electron gas in 3 dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. In equivalent way one can optimize the Gagliardo--Nirenberg inequality subject to the constraint fixing the $L^2$ norm. The uniqueness of the minimizers for the case $p=2$, i.e. for the case of Hartree--Choquard is well known. The main difficulty for the case $p > 2$ is connected with possible lack of control on the $L^p$ norm of the minimizers., Comment: Some misprints have been corrected

Published
2019

3. Decay and Scattering in energy space for the solution of weakly coupled Schr\'odinger-Choquard and Hartree-Fock equations

Author

Tarulli, Mirko and Venkov, George

Subjects
Mathematics - Analysis of PDEs, Mathematical Physics
Abstract

We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space for the solutions to the systems of $N$ defocusing Schr\"odinger-Choquard equations with mass-energy intercritical nonlinearities in any space dimension and of defocusing Hartree-Fock equations, for any dimension $d\geq3$., Comment: Typos fixed, other references added

Published
2019

4. Existence and uniqueness of ground states for $p$ - Choquard model in 3D

Author

Georgiev, Vladimir, Tarulli, Mirko, and Venkov, George

Subjects
Mathematics - Analysis of PDEs, 35Q51, 35Q40, 35Q55, 49S05
Abstract

We study the $p$-Choquard equation in 3-dimensional case and establish existence and uniqueness of ground states for the corresponding Weinstein functional. For proving the uniqueness of ground states, we use the radial symmetry to transform the equation into an ordinary differential system, and applying the Pohozaev identities and Gronwall lemma we show that any two Weinstein minimizers coincide., Comment: 13

Published
2018
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7. Symmetry and uniqueness of minimizers of Hartree type equations with external Coulomb potential

Author

Georgiev, Vladimir and Venkov, George

Subjects
Mathematics - Analysis of PDEs
Abstract

In the present article we study the radial symmetry of minimizers of the energy functional, corresponding to the repulsive Hartree equation in external Coulomb potential. To overcome the difficulties, resulting from the "bad" sign of the nonlocal term, we modify the reflection method and then, by using Pohozaev integral identities we get the symmetry result.

Published
2010

8. On a Generalized Gagliardo–Nirenberg Inequality with Radial Symmetry and Decaying Potentials.

Author

Tarulli, Mirko and Venkov, George

Subjects
*SYMMETRY, *NONLINEAR Schrodinger equation
Abstract

We present a generalized version of a Gagliardo–Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behavior. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with H s -subcritical nonlinearities, either of a local or nonlocal nature. [ABSTRACT FROM AUTHOR]

Published
2024
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13. On the Decay of Solutions to a Class of Hartree Equations

Author

Tarulli, Mirko and Venkov, George

Subjects
Non-linear Schrödinger еquations, Morawetz inequalities, Hartree equations
Abstract

[Venkov George; Венков Георги] 2010 Mathematics Subject Classification: 35Q55, 34G20, 35P25.

Published
2019

14. A Fractional Inequality on Compact Manifolds and Lie Groups

Author

Tarulli, Mirko and Venkov, George

Subjects
A-priori estimates on Riemannian manifolds, Sobolev spaces on Riemannian manifolds
Abstract

[Venkov George; Венков Георги] 2010 Mathematics Subject Classification: 35B45, 53B20.

Published
2018

16. Optimal Interpolation Constant for the Generalized Schrödinger-Newton System

Author

Georgiev, Vladimir and Venkov, George

Subjects
Schrödinger-Newton system, radially symmetric solutions, generalized Choquard equation, shooting method, energy minimizers
Abstract

[Georgiev Vladimir; Георгиев Владимир]; [Venkov George; Венков Георги] 2010 Mathematics Subject Classification: 35A05, 35A15, 35Q51, 35Q55.

Published
2015

17. Глобални резултати за решението на уравнението на шрьодингер с критична маса и нелинейност от конволюционен тип в R^n

Author

Venkov, George and Genev, Hristo

Subjects
Scattering, Critical Mass, Nonlinear Schrödinger Equation, Local and Global Existence, Convolution Nonlinearity
Abstract

Георги Венков, Христо Генев - Разглеждаме един клас от L^2 - критични нелинейни уравнения на Шрьодингер в R^(1+n) с конволюционна нелинейност от тип Хартри. Целта ни е да установим локалното и глобално съществуване на решенията, както и коректност на задачата на Коши в достатъчно малка околност на нулата в пространството L^2 (R^n). Като естествено следствие на глобалните резултати ние доказваме съществуване на оператор на разсейване за малки начални условия. We are concerned with a class of L^2 - critical nonlinear Schrödinger equations in R^(1+n) with convolution nonlinearity of Hartree type. We aim to establish local and global existence and well-posedness of solutions in a small neighborhood of the origin in L^2 (R^n). As a natural consequence of the global results, we prove the existence of scattering operator for small initial data. *2000 Mathematics Subject Classification: 35A05, 35Q55. The second author is partially supported by the Research Sector of FMI-SU, contract number: 028/2009.

Published
2010

18. High-quality Light Field Interpolation in Epipolar Plane Image Domain by DCT-based Shearing

Author

Atanas Gotchev, Leonid Bilevich, Suren Vagharshakyan, Venkov, George, Pasheva, Vesela, Tampere University, Department of Signal Processing, Research group: 3D MEDIA, Doctoral Programme in Computing and Electrical Engineering, and Signal Processing Research Community (SPRC)

Subjects
Cardinal point, Plane (geometry), Computer Science::Computer Vision and Pattern Recognition, Epipolar geometry, Physics::Medical Physics, Discrete cosine transform, Geometry, 113 Computer and information sciences, Domain (mathematical analysis), Light field, Mathematics, Interpolation, View synthesis
Abstract

Light field (LF) is a 4-D function representing the light radiance in free space in terms of rays. A dense grid of cameras, parameterized by two planes, captures an LF: the sensor plane and the focal plane. Multi-camera images stack in volumes, and when sliced, form epipolar plane images (EPI). In EPI, lines with the same slope represent object points at the same scene depth. Thus, the synthesis of new views can be formulated as a problem of interpolation in EPI domain. In this contribution, we propose a three-pass algorithm for LF interpolation in EPI domain. Each EPI is sheared by a factor determined by the dominant slope, employing fast DCT-based fractional shifts. In sheared EPI, dominant lines appear vertical and can be easily interpolated. 'De-shearing' reconstructs EPI's original geometry. We analyze the performance of the proposed LF interpolation in Fourier domain and illustrate it with examples of virtual view synthesis from dense multi-camera imagery.

Published
2014

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