13 citations · 43 across the 13 of their papers we have counts for
14 papers
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…
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…
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…
The regularity problem for parabolic operators
Martin Dindoš, Linhan Li, Jill Pipher
In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $-\partial_tu + \mbox{div}(A\nabla u)=0$ on a Lipschitz cylinder $\mathcal O\ti…
The Poisson-Neumann problem and its relation to the Neumann problem
Joseph Feneuil, Linhan Li
We introduce the Poisson-Neumann problem for an uniformly elliptic operator in divergence form in a bounded 1-sided Chord Arc Domain , which consider…
A Green function characterization of uniformly rectifiable sets of any codimension
Joseph Feneuil, Linhan Li
In this paper, we obtain a unified characterization of uniformly rectifiable sets of {\it any codimension} in terms of a Carleson estimate on the second derivatives of the Green fu…
Green functions and smooth distances
Joseph Feneuil, Linhan Li, Svitlana Mayboroda
In the present paper, we show that for an optimal class of elliptic operators with non-smooth coefficients on a 1-sided Chord-Arc domain, the boundary of the domain is uniformly re…
Small results for Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider elliptic operators in a domain bounded by a chord-arc surface with small enough constant, and whose coefficients $A…
Carleson estimates for the Green function on domains with lower dimensional boundaries
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider an elliptic divergence form operator in with and prove that its Green function is almost affine, in th…
Carleson measure estimates for the Green function
Guy David, Linhan Li, Svitlana Mayboroda
In the present paper, we consider an elliptic divergence form operator in the half-space and prove that its Green function is almost affine, or more precisely, that the normalized…
The Dirichlet problem for elliptic operators having a BMO anti-symmetric part
Steve Hofmann, Linhan Li, Svitlana Mayboroda +1
The present paper establishes the first result on the absolute continuity of elliptic measure with respect to the Lebesgue measure for a divergence form elliptic operator with non-…
theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part
Steve Hofmann, Linhan Li, Svitlana Mayboroda +1
We consider the operator , where the matrix is real-valued, elliptic, with the symmetric part of in , and the ant…
Decoupling in for curves with Vanishing Curvature
Chandan Biswas, Maxim Gilula, Linhan Li +2
We expand the class of curves for which the decoupling conjecture holds for . Our class of curves includes all real-analytic r…
Boundary behavior of solutions of elliptic operators in divergence form with a BMO anti-symmetric part
Linhan Li, Jill Pipher
In this paper, we investigate the boundary behavior of solutions of divergence-form operators with an elliptic symmetric part and a anti-symmetric part. Our results will hold…