6 papers
Elliptic theory and dimension drop for operators with divergence-free form-bounded drifts in one-sided chord-arc domains
Svitlana Mayboroda, Alberto Pacati
We develop a boundary value and potential theory for elliptic operators \[ L=-\Div(A\nabla)+\B\cdot\nabla \] with form-bounded drift in one-sided chord-arc domains. Assuming that t…
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…
Robin harmonic measure with a variable permeability parameter
Svitlana Mayboroda, Alberto Pacati
In this paper we study the behavior of the solutions to the Robin problem in bounded -sided NTA domains with Ahlfors-David regular boundary, generalizing the results of \cite{Da…
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…
Some remarks on singular capillary cones with free boundary
Alberto Pacati, Giorgio Tortone, Bozhidar Velichkov
We study singular minimizing capillary cones with free boundary. We provide a stability criterion Jerison-Savin and use it to prove that a minimizing capillary cone is flat whe…