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Irene Drelichman

Publications and source records attributed to Irene Drelichman.

18 recordsLinked to original sources
arXiv2026

The Fractional Korn Inequality on Uniform Domains and New Korn Inequalities for Truncated Seminorms

We prove the so-called second case of the fractional Korn inequality for uniform domains. We obtain this result as an application of a novel fractional Korn-type inequality formulated in terms of truncated seminorms, which turns out to be valid for the broader class of John domains. We also obtain weighted estimates in which the weights are certain powers of the distance to the boundary that depend on the fractional exponent and the Assouad codimension of the boundary of the domain.

math.AP↗
arXiv2024

An interpolation result for $A_1$ weights with applications to fractional Poincaré inequalities

We characterize the real interpolation space between weighted $L^1$ and $W^{1,1}$ spaces on arbitrary domains different from $\mathbb{R}^n$, when the weights are positive powers of the distance to the boundary multiplied by an $A_1$ weight. As an application of this result we obtain weighted fractional Poincaré inequalities with sharp dependence on the fractional parameter $s$ (for $s$ close to 1) and show that they are equivalent to a weighted Poincaré inequality for the gradient.

math.CA↗
arXiv2024

Stability of the Ritz projection in weighted $W^{1,1}$

We prove the stability in weighted $W^{1,1}$ spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt's class $A_1$ and the family of meshes is quasi-uniform.

math.NA↗
arXiv2019

Improved fractional Poincaré type inequalities on John domains

We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $μ$ under some mild regularity conditions on the measure $μ$. We also give sufficient conditions on a bounded domain to support fractional Poincaré type inequalities in this setting.

math.CA↗
arXiv2018

A weighted setting for the numerical approximation of the Poisson problem with singular sources

We consider the approximation of Poisson type problems where the source is given by a singular measure and the domain is a convex polygonal or polyhedral domain. First, we prove the well-posedness of the Poisson problem when the source belongs to the dual of a weighted Sobolev space where the weight belongs to the Muckenhoupt class. Second, we prove the stability in weighted norms for standard finite element approximations under the quasi-uniformity assumption on the family of meshes.

math.NA↗
arXiv2018

Weighted Inequalities for the Fractional Laplacian and the Existence of Extremals

In this article we obtain improved versions of Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities, involving Besov norms of negative smoothness. As an application of the former, we derive the existence of extremals of the Stein-Weiss inequality in certain cases, some of which are not contained in the celebrated theorem of E. Lieb.

math.AP↗
arXiv2017

On the interpolation space $(L^p(Ω), W^{1,p}(Ω))_{s,p}$ in non-smooth domains

We show that, for certain non-smooth bounded domains $Ω\subset\mathbb{R}^n$, the real interpolation space $(L^p(Ω), W^{1,p}(Ω))_{s,p}$ is the subspace $\widetilde W^{s,p}(Ω) \subset L^p(Ω)$ induced by the restricted fractional seminorm $$ |f|_{\widetilde W^{s,p}(Ω)} = \Big( \int_Ω\int_{|x-y|<\frac{d(x)}2} \frac{|f(x)-f(y)|^p}{|x-y|^{n+sp}} \, dy \,dx \Big)^\frac{1}{p}. $$ In particular, the above result includes simply connected uniform domains in the plane, for which a characterization of the interpolation space was previously unknown.

math.CA↗
arXiv2013

Weighted convolution inequalities for radial functions

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of radial functions in weighted Lorentz spaces and embedding theorems for radial Besov spaces with power weights.

math.CA↗
arXiv2011

Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions

We present a new criterion for the weighted $L^p-L^q$ boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates for Laguerre and Hermite fractional integrals with a unified and simpler approach.

math.CA↗
arXiv2007

Improved Poincare inequalities with weights

In this paper we prove that if $Ω\in\mathbb{R}^n$ is a bounded John domain, the following weighted Poincare-type inequality holds: $$ \inf_{a\in \mathbb{R}}\| (f(x)-a) w_1(x) \|_{L^q(Ω)} \le C \|\nabla f(x) d(x)^αw_2(x) \|_{L^p(Ω)} $$ where $f$ is a locally Lipschitz function on $Ω$, $d(x)$ denotes the distance of $x$ to the boundary of $Ω$, the weights $w_1, w_2$ satisfy certain cube conditions, and $α\in [0,1]$ depends on $p,q$ and $n$. This result generalizes previously known weighted inequalities, which can also be obtained with our approach.

math.CA↗