arXiv subjects

María Eugenia Cejas

Publications and source records attributed to María Eugenia Cejas.

4 recordsLinked to original sources

arXiv2026

Solvability of divergence equation in Lipschitz spaces

We study the solvability of the divergence equation $$ \operatorname{div} \u = f $$ in bounded $C^2$ domains under homogeneous Dirichlet boundary conditions for data $f\in C^{0,α}(Ω)$ satisfying the compatibility condition $ \int_Ωf =0. $ We construct a solution $\u$ such that for every $0<β<α$ $$ \u\in C^{1,β}(Ω)^n $$ satisfies $$ \|\u\|_{C^{1,β}(Ω)} \le C\|f\|_{C^{0,α}(Ω)}. $$ The proof combines localization techniques with a boundary flattening procedure reducing the problem to a model half-cube.

math.AP↗

arXiv2024

Solutions of the divergence equation in Hardy and lipschitz spaces

Given a bounded domain $Ø$ and $f$ of zero integral, the existence of a vector fields $\u$ vanishing on $\partialØ$ and satisfying $\d\u=f$ has been widely studied because of its connection with many important problems. It is known that for $f\in L^p(Ø)$, $1<p<\infty$, there exists a solution $\u\in W^{1,p}_0(Ø)$, and also that an analogous result is not true for $p=1$ or $p=\infty$. The goal of this paper is to prove results for Hardy spaces when $\frac{n}{n+1}<p\le 1$, and in the other limiting case, for bounded mean oscillation and Lipschitz spaces. As a byproduct of our analysis we obtain a Korn inequality for vector fields in Hardy-Sobolev spaces.

math.AP↗

arXiv2021

Some non-standard biparametric Poincaré type inequalities through harmonic analysis

We show some non-standard Poincaré type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions and fractional integrals. We also provide a sharper result by using extrapolation techniques.

math.CA↗

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↗