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math.AP2026
The homogeneous and inhomogeneous Dirichlet problem
David S. Jerison, Carlos E. Kenig
We revisit the homogeneous and inhomogeneous Dirichlet problem for the Laplacian on Lipschitz domains. This is motivated by the recent postings by Amrouche and Moussaoui which purp…
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…