7 citations · 12 across the 5 of their papers we have counts for
8 papers · 1 filter
Singularity formation and self-shrinkers for the parabolic Bernoulli problem
Hunter Liu, Sebastian Munoz, Zihui Zhao
We study singularity formation for classical solutions of the parabolic Bernoulli free boundary problem and the associated self-similar profiles. Inspired by Ricci and mean curvatu…
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…
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…
Dirichlet problem in domains with lower dimensional boundaries
Joseph Feneuil, Svitlana Mayboroda, Zihui Zhao
The present paper pioneers the study of the Dirichlet problem with boundary data for second order operators with complex coefficients in domains with lower dimensional bounda…