4 papers
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…
A Variable Coefficient Free Boundary Problem for -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 is the region above the graph of a…
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 . Sp…
Carleson measure estimates, corona decompositions, and perturbation of elliptic operators without connectivity
Mingming Cao, Pablo Hidalgo-Palencia, José María Martell
Let be an open set with Ahlfors-David regular boundary satisfying the corkscrew condition. When is connected in some quantitative form one can establish that for any real e…