2 papers
math.AP2024
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…
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 $…