33 citations · 69 across the 21 of their papers we have counts for
30 papers
Findings-aware Language-Image Pretraining for CT Volume Interpretation
Takuro Shimaya, Junya Inoh, Masahiro Saiko
Computed tomography (CT) provides diverse patient information and various clinical tasks, for which numerous deep learning models have been investigated. Recent years have seen the…
Explicit sharp gradient stability of the -Poincaré inequality and fundamental gaps for the Dirichlet -Laplacian operator
Nurgissa Yessirkegenov, Amir Zhangirbayev
In this paper, we establish sharp gradient stability of the -Poincaré inequality with explicit constants on bounded convex domains for any . These estimates cont…
Sharp forms and quantitative stability for general weighted discrete -Hardy inequalities
Nurgissa Yessirkegenov, Amir Zhangirbayev
In this paper, we provide a sharp remainder term for the general weighted discrete -Hardy inequality. By choosing appropriate weights and specifying , we are able to…
Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for
Yerkin Shaimerdenov, Nurgissa Yessirkegenov, Amir Zhangirbayev
Inspired by the work of Cossetti and D'Arca [CD25], we show that the general weighted -Hardy type inequalities [CD25, Theorems 1.1 and 1.2] and the corresponding identities…
Stability of the -Poincaré inequality for the Lebesgue measure and Gaussian probability measure with explicit geometric dependence and applications to spectral gaps
Nurgissa Yessirkegenov, Amir Zhangirbayev
In this paper, we obtain stability results for the -Poincaré inequality for both Lebesgue measure and Gaussian probability measure (Theorem 3.3 and Theorem 3.13) that involv…
Sharp remainder terms and stability of weighted Hardy-Poincaré and Heisenberg-Pauli-Weyl inequalities related to the Baouendi-Grushin operator
Yerkin Shaimerdenov, Nurgissa Yessirkegenov, Amir Zhangirbayev
In this paper, we obtain sharp remainder terms for the Hardy-Poincaré inequalities with general non-radial weights in the setting of Baouendi-Grushin vector fields (see Theorem 2.5…
Sharp remainder of the -Poincaré inequality for Baouendi-Grushin vector fields
Kuralay Apseit, Nurgissa Yessirkegenov, Amir Zhangirbayev
In this paper, we establish a sharp remainder formula for the Poincaré inequality for Baouendi-Grushin vector fields in the setting of for complex-valued functions. In spec…
A comparison principle for nonlinear parabolic equations with nonlocal source and gradient absorption
Zhaniya Amirzhankyzy, Nurgissa Yessirkegenov
This paper investigates the initial-boundary value problem for a nonlinear parabolic equation involving the -Laplacian operator, nonlocal source terms, gradient absorption, and…
Refined general weighted -Hardy and Caffarelli-Kohn-Nirenberg type inequalities and identities related to the Baouendi-Grushin operator
Nurgissa Yessirkegenov, Amir Zhangirbayev
In this paper, we present a sufficient condition on a pair of nonnegative weights and such that we have a general weighted -Hardy type identity. The result, for a ce…
Cylindrical extensions of critical Sobolev type inequalities and identities
Michael Ruzhansky, Yerkin Shaimerdenov, Nurgissa Yessirkegenov
In this paper, we investigate cylindrical extensions of critical Sobolev type (improved Hardy) inequalities and identities in the style of Badiale-Tarantello [BT02], which in a spe…
Cylindrical Hardy, Sobolev type and Caffarelli-Kohn-Nirenberg type inequalities and identities
Madina Kalaman, Nurgissa Yessirkegenov
In this paper we discuss cylindrical extensions of improved Hardy, Sobolev type and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants and identities in the spirit of…
Critical, stability and higher-order analysis for Hardy type inequalities on Cartan-Hadamard manifolds
Prasun Roychowdhury, Durvudkhan Suragan, Nurgissa Yessirkegenov
In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan-Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain…
Unified weighted Hardy-type inequalities
Durvudkhan Suragan, Nurgissa Yessirkegenov
We present a unified approach to obtain Hardy-type inequalities in the context of nilpotent Lie groups with sharp constants. The unified methodology employed herein allows for expl…
A comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow…
Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications
Andrei Velicu, Nurgissa Yessirkegenov
In this paper we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Trudinger, Caffarelli-Kohn-Nirenberg inequalities and the uncertainty principle for Dunkl opera…
Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we study the global well-posedness of the following Cauchy problem on a sub-Riemannian manifold : \begin{equation*} \begin{cases} u_{t}-\mathfrak{L}_{M} u=f(u), \;…
Very weak solutions to hypoelliptic wave equations
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we study the Cauchy problem for the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups when the time-dependent non-negative pro…
Hardy-Sobolev-Rellich, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy-Littlewood-Sobolev, Caffarelli-Kohn-Nirenberg, Gagliardo-Nirenberg inequaliti…
Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups
Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov
In this paper we describe the Euler semigroup on homogeneous Lie groups, which allows us to obtain various types of the Hardy-Sobolev and…
Hypoelliptic functional inequalities
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalitie…
Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional cur…
Critical Gagliardo-Nirenberg, Trudinger, Brezis-Gallouet-Wainger inequalities on graded groups and ground states
Michael Ruzhansky, Nurgissa Yessirkegenov
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded Lie gro…
Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov
In this short paper, we establish a range of Caffarelli-Kohn-Nirenberg and weighted -Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with s…
Rellich inequalities for sub-Laplacians with drift
Michael Ruzhansky, Nurgissa Yessirkegenov
In this note we prove horizontal weighted Rellich inequalities for the sub-Laplacian and for sub-Laplacians with drift on general stratified groups. We show how the presence of a d…