Pablo Hidalgo-Palencia

activity

20222026

collaborators

8 papers

math.AP2026

Boundary regularity of harmonic functions in $C^{1}$ slit domains

Joan Domingo-Pasarin, Pablo Hidalgo-Palencia, Alejandro Martínez +1

We establish precise upper and lower estimates for harmonic functions vanishing on the slit of a $C^{1}$ slit domain, with no assumption that the slit lies in a hyperplane. The class…

math.AP2026

Parabolic uniform rectifiability is characterized by Carleson measure estimates for bounded caloric functions

Simon Bortz, Pablo Hidalgo-Palencia, Steve Hofmann +1

We show that the parabolic uniform rectifiability of a set can be characterized by an interior PDE property, namely Carleson measure estimates for bounded solutions to the heat equ…

math.AP2025

The parabolic Dirichlet problem with continuous and Hölder boundary data, and rough coefficients

Pablo Hidalgo-Palencia, Cody Hutcheson, Joseph Kasel

We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the Hölder Dirichlet problem…

math.AP2025

A Variable Coefficient Free Boundary Problem for $L^{p}$ -solvability of Parabolic Dirichlet Problems in Graph Domains

Simon Bortz, Sandra Ferris, Pablo Hidalgo-Palencia +1

We investigate variable coefficient analogs of a recent work of Bortz, Hofmann, Martell and Nyström [BHMN25]. In particular, we show that if $Ω$ is the region above the graph of a…

math.AP2024

Positive solutions to general semilinear overdetermined boundary problems

Alberto Enciso, Pablo Hidalgo-Palencia, Xavier Ros-Oton

We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $Ω \subset R^{n}$ . Sp…

math.AP2023

Elliptic operators in rough sets, and the Dirichlet problem with boundary data in Hölder spaces

Mingming Cao, Pablo Hidalgo-Palencia, José María Martell +2

In this paper we study the Dirichlet problem for real-valued second order divergence form elliptic operators with boundary data in Hölder spaces. Our context is that of open sets $…

math.AP2023

On the Kato problem for elliptic operators in non-divergence form

Luis Escauriaza, Pablo Hidalgo-Palencia, Steve Hofmann

We consider the Kato square root problem for non-divergence second order elliptic operators $L = - a_{ij} D_{i} D_{j}$ , and, especially, the normalized adjoints of such operators. In par…

math.CA2022

Carleson measure estimates, corona decompositions, and perturbation of elliptic operators without connectivity

Mingming Cao, Pablo Hidalgo-Palencia, José María Martell

Let $Ω$ be an open set with Ahlfors-David regular boundary satisfying the corkscrew condition. When $Ω$ is connected in some quantitative form one can establish that for any real e…