arXiv subjects

Paola Vernole

Publications and source records attributed to Paola Vernole.

4 recordsLinked to original sources

arXiv2018

Magnetostatic problems in fractal domains

We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal one. We consider the numerical approximation of the pre-fractal problems via FEM and we prove a priori error estimates. Some numerical simulations are also shown. Our long term motivation includes studying problems that appear in quantum physics in fractal domains.

math-ph↗

arXiv2017

Nonlocal Venttsel' diffusion in fractal-type domains: regularity results and numerical approximation

We study a nonlocal Venttsel' problem in a non-convex bounded domain with a Koch-type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical approximation of the problem is carried out and optimal a priori error estimates are obtained.

math.AP↗

arXiv2017

On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains

We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional domains.

math.AP↗

arXiv2016

Fractal snowflake domain diffusion with boundary and interior drifts

We study a parabolic Ventsell problem for a second order differential operator in divergence form and with interior and boundary drift terms on the snowflake domain. We prove that under standard conditions a related Cauchy problem possesses a unique classical solution and explain in which sense it solves a rigorous formulation of the initial Ventsell problem. As a second result we prove that functions that are intrinsically Lipschitz on the snowflake boundary admit Euclidean Lipschitz extensions to the closure of the entire domain. Our methods combine the fractal membrane analysis, the vector analysis for local Dirichlet forms and PDE on fractals, coercive closed forms, and the analysis of Lipschitz functions.

math.AP↗