7 citations · 8 across the 6 of their papers we have counts for
5 papers · 1 filter
On the asymptotic properties of solutions to one-phase free boundary problems
Max Engelstein, Daniel Restrepo, Zihui Zhao
In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an i…
A note on the critical set of harmonic functions near the boundary
Carlos Kenig, Zihui Zhao
Let be a harmonic function in a domain , which vanishes on an open subset of the boundary. In this note we study its critical set $\{x \in \overlin…
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 $…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper, along with its companion [Hofmann, Martell, Mayboroda, Toro, Zhao, arXiv:1710.06157], establishes the correspondence between the properties of the solutions of a…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part I: The small constant case
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper, along with its sequel, establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We…