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

@article{Creo2019OnTN, title={On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains}, author={Simone Creo and Maria Rosaria Lancia and Alexander I. Nazarov and Paola Vernole}, journal={Discrete \& Continuous Dynamical Systems - S}, year={2019} }

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

## 7 Citations

### Venttsel Boundary Value Problems with Discontinuous Data

- MathematicsSIAM J. Math. Anal.
- 2021

Maximal regularity and strong solvability in Sobolev spaces are proved in linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients.

### Regularity results for nonlocal evolution Venttsel’ problems

- Mathematics
- 2020

Abstract We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev…

### Nonlocal Venttsel' diffusion in fractal‐type domains: Regularity results and numerical approximation

- MathematicsMathematical Methods in the Applied Sciences
- 2019

We study a nonlocal Venttsel' problem in a nonconvex bounded domain with a Koch‐type boundary. Regularity results of the strict solution are proved in weighted Sobolev spaces. The numerical…

### Approximation of 3D Stokes Flows in Fractal Domains

- MathematicsFractals in Engineering: Theoretical Aspects and Numerical Approximations
- 2020

We study a Stokes flow in a cylindrical-type fractal domain with homogeneous Dirichlet boundary conditions. We consider its numerical approximation by mixed methods: finite elements in space and…

### Magnetostatic Problems in Fractal Domains

- MathematicsAnalysis, Probability and Mathematical Physics on Fractals
- 2020

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…

### Singular $p$-Homogenization for Highly Conductive Fractal Layers

- MathematicsZeitschrift für Analysis und ihre Anwendungen
- 2021

We consider a quasi-linear homogenization problem in a two-dimensional prefractal domain Ωn, for n ∈ N, surrounded by thick fibers of amplitude ε. We introduce a sequence of “pre-homogenized” energy…

### On the solvability of a two-dimensional Ventcel problem with variable coefficients

- Mathematics
- 2020

This paper deals with the following mixed boundary value problem \begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} \begin{cases} -\Delta u = f &\mbox{in $\Omega$,} \\ u = \varphi &\mbox{on…

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