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

Simone Creo; Maria Rosaria Lancia; Alexander Nazarov; Paola Vernole

doi:10.3934/dcdss.2019004

Article Contents

2019, Volume 12, Issue 1: 57-64. Doi: 10.3934/dcdss.2019004

This issue Previous Article Asymptotics for quasilinear obstacle problems in bad domains Next Article Convergence and density results for parabolic quasi-linear Venttsel' problems in fractal domains

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

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Università degli studi di Roma Sapienza, Via A. Scarpa 16, 00161 Roma, Italy
2.
St. Petersburg Department of Steklov Mathematical Institute, and St. Petersburg State University, Fontanka 27, and Universitetskii pr. 28, 191023 St. Petersburg, Russia and 198504 St. Petersburg, Russia
3.
Dipartimento di Matematica, Università degli Studi di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy

* Corresponding author: Paola Vernole
* Corresponding author: Paola Vernole

Received: January 31, 2017

Revised: July 31, 2017

Published: July 2018

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Abstract

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

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Mathematics Subject Classification: Primary: 35J25, 35B65; Secondary: 35R02, 35B45.

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Figure 1. A possible example of domain $\Omega$. In this case $N=9$ and $\alpha=\alpha_7$

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References

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