7 citations · 12 across the 4 of their papers we have counts for
9 papers
Examples of non-Dini domains with large singular sets
Carlos Kenig, Zihui Zhao
Let be a non-trivial harmonic function in a domain which vanishes on an open set of the boundary. In a recent paper, we showed that if is a -Di…
Expansion of harmonic functions near the boundary of Dini domains
Carlos Kenig, Zihui Zhao
Let be a harmonic function in a -Dini domain, such that vanishes on an open set of the boundary. We show that near every point in the open set, can be written uniq…
Elliptic measures for Dahlberg-Kenig-Pipher operators: Asymptotically optimal estimates
Simon Bortz, Tatiana Toro, Zihui Zhao
Questions concerning quantitative and asymptotic properties of the elliptic measure corresponding to a uniformly elliptic divergence form operator have been the focus of recent stu…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of w…
Two Phase Free Boundary Problem for Poisson Kernels
Simon Bortz, Max Engelstein, Max Goering +2
We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, th…
Dirichlet energy-minimizers with analytic boundary
Camillo De Lellis, Zihui Zhao
In this paper, we consider multi-valued graphs with a prescribed real analytic interface that minimize the Dirichlet energy. Such objects arise as a linearized model of area minimi…