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math.AP2026
The Neumann problem for parabolic operators with coefficients satisfying small Carleson condition
Martin Dindoš, Linhan Li, Jill Pipher
In this paper, we resolve the question of whether the Neumann problem for the parabolic PDE on a Lipschitz cylinder $\mathcal O\times\mat…
math.AP2026
Stability of Dirichlet problem under small bi-Lipschitz transformations of domains
Joseph Feneuil, Linhan Li, Jinping Zhuge
We show that small bi-Lipschitz deformations of a Lipschitz domain (with possibly large Lipschitz constant) preserve the solvability of the Dirichlet problem for the Laplacian with…
math.AP2026
Localization and interpolation of parabolic Neumann problems
Martin Dindoš, Linhan Li, Jill Pipher
We show a localization estimate for local solutions to the parabolic equation $-\partial_t u+\mbox{div} (A\nabla u)=0$ with zero Neumann data, assuming that the Neumann probl…