# American Institute of Mathematical Sciences

February  2019, 12(1): 57-64. doi: 10.3934/dcdss.2019004

## 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

Received  February 2017 Revised  August 2017 Published  July 2018

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

Citation: Simone Creo, Maria Rosaria Lancia, Alexander Nazarov, Paola Vernole. On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 57-64. doi: 10.3934/dcdss.2019004
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##### References:
A possible example of domain $\Omega$. In this case $N=9$ and $\alpha=\alpha_7$
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