Related papers: Hyperplane integrability conditions and smoothing …

We introduce "superheated integrability," which produces characteristic staircase transmission plots for barrier collisions of breathers of the nonlinear Schr\"odinger equation. The effect makes tangible the inverse scattering transform,…

Extending the methods developed in the author's previous paper and using adapted coordinate systems in two variables, an L^p boundedness theorem is proven for maximal operators over hypersurfaces in R^3 when p > 2. When the best possible p…

We study hyperinterpolation and its spectral multiplier variants on the sphere under weak cubature assumptions formulated through Sobolev discrepancy estimates. In contrast with classical hyperinterpolation theory, our framework does not…

We investigate weighted Sobolev regularity of weak solutions of non-homogeneous parabolic equations with singular divergence-free drifts. Assuming that the drifts satisfy some mild regularity conditions, we establish local weighted…

In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A_p-condition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for…

We prove the Hardy-Littlewood-Sobolev type $L^p$ estimates for the gain term of the Boltzmann collision operator including Maxwellian molecule, hard potential and hard sphere models. Combining with the results of Alonso et al. [2] for the…

In the present paper we extend the $L^2$ Korn interpolation and second inequalities in thin domains, proven in [\ref{bib:Harutyunyan.4}], to the space $L^p$ for any $1<p<\infty.$ A thin domain in space is roughly speaking a shell with…

We prove $L^2 \to L^p$ estimates on the torus for maximal polynomial modulations of Calder\'on-Zygmund operators with anisotropic scaling. We obtain improved constants in these estimates. As a corollary, maximal polynomial modulations of a…

We investigate the interior Sobolev regularity of weak solutions to the nonlocal $(1, p)$-Laplace equations in the superquadratic case $p\ge 2$. As a product, the explicit H\"{o}lder continuity estimates of weak solutions are derived. The…

In this paper we consider the $L_q$-approximation of multivariate periodic functions $f$ with $L_p$-bounded mixed derivative (difference). The (possibly non-linear) reconstruction algorithm is supposed to recover the function from function…

We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…

We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal…

We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…

We show the existence of solution in the maximal $L_p-L_q$ regularity framework to a class of symmetric parabolic problems on a uniformly $C^2$ domain in ${\mathcal R}$. Our approach consist in showing ${\mathcal R}$ - boundedness of…

In this article, we consider the limited data problem for spherical mean transform. We characterize the generation and strength of the artifacts in a reconstruction formula. In contrast to the third's author work [Ngu15b], the observation…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…

We consider degenerate and singular parabolic equations with $p$-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity…

The problem of $L^p(R^3)\to L^2(S)$ Fourier restriction estimates for smooth hypersurfaces S of finite type in R^3 is by now very well understood for a large class of hypersurfaces, including all analytic ones. In this article, we take up…

We study mapping properties of finite field k-plane transforms. Using geometric combinatorics, we do an elaborate analysis to recover the critical endpoint estimate. As a consequence, we obtain optimal L^p-L^r estimates for all k-plane…

In this article, we address the challenge of solving the ill-posed reconstruction problem in computed tomography using a translation invariant diagonal frame decomposition (TI-DFD). First, we review the concept of a TI-DFD for general…