15 citations · 31 across the 16 of their papers we have counts for
20 papers
The Dirichlet problem with boundary data of fractional smoothness in domains with Ahlfors regular boundary
Ariel Barton, Svitlana Mayboroda, Alberto Pacati
We establish well posedness of the Dirichlet problem in weak local John domains $Ω\subset\R^\dmn$ with Ahlfors regular boundaries of possibly non integer dimension $0<\bdmn<\dmn$,…
The Poisson problem in domains with Ahlfors regular boundary
Ariel Barton, Svitlana Mayboroda, Alberto Pacati
We establish well posedness of the Poisson problem in weak local John domains, for linear second order elliptic equations with real coefficients, and with data in weighted Lebesgue…
The Poisson-Dirichlet problem in domains with Ahlfors regular boundary
Ariel Barton, Svitlana Mayboroda, Alberto Pacati
We present an announcement of some recent results concerning well-posedness of the Poisson-Dirichlet problem with boundary data in Besov spaces with fractional smoothness. This is…
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…