arXiv subjects

Ricardo Durán

Publications and source records attributed to Ricardo Durán.

3 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↗

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↗

arXiv2013

Powers of distances to lower dimensional sets as Muckenhoupt weights

Let $(X,d,μ)$ be an Ahlfors metric measure space. We give sufficient conditions on a closed set $F\subseteq X$ and on a real number $β$ in such a way that $d(x,F)^β$ becomes a Muckenhoupt weight. We give also some illustrations to regularity of solutions of partial differential equations and regarding some classical fractals.

math.FA↗