15 citations · 18 across the 7 of their papers we have counts for
8 papers · 1 filter
Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms
Ariel Barton, Michael Duffy
We establish the Caccioppoli inequality, a reverse Hölder inequality in the spirit of the classic estimate of Meyers, and construct the fundamental solution for linear elliptic dif…
The Neumann problem for higher order elliptic equations
Ariel Barton
We solve the Neumann problem in the half space , for higher order elliptic differential equations with variable self-adjoint -independent coefficients, and w…
Nontangential estimates on layer potentials and the Neumann problem for higher order elliptic equations
Ariel Barton, Steve Hofmann, Svitlana Mayboroda
We solve the Neumann problem, with nontangential estimates, for higher order divergence form elliptic operators with variable -independent coefficients. Our results are accompan…
Extrapolation of well posedness for higher order elliptic systems with rough coefficients
Ariel Barton
In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We establish well posedness for problems with boundary data in B…
Layer potentials for general linear elliptic systems
Ariel Barton
In this paper we construct layer potentials for elliptic differential operators using the Lax-Milgram theorem, without recourse to the fundamental solution; this allows layer poten…
Dirichlet and Neumann boundary values of solutions to higher order elliptic equations
Ariel Barton, Steve Hofmann, Svitlana Mayboroda
We show that if is a solution to a linear elliptic differential equation of order in the half-space with -independent coefficients, and if satisfies certain a…