Transmission problems for the fractional $ p $-Laplacian across fractal interfaces

Simone Creo; Maria Rosaria Lancia; Paola Vernole

doi:10.3934/dcdss.2022047

Article Contents

2022, Volume 15, Issue 12: 3621-3644. Doi: 10.3934/dcdss.2022047

This issue Previous Article On some qualitative aspects for doubly nonlocal equations Next Article Stability and errors estimates of a second-order IMSP scheme

Transmission problems for the fractional $ p $-Laplacian across fractal interfaces

Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Via A. Scarpa 10, 00161 Roma, Italy

^* Corresponding author: Maria Rosaria Lancia
^* Corresponding author: Maria Rosaria Lancia

Received: October 2021

Revised: January 2022

Early access: March 8, 2022

Published online: March 8, 2022

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Abstract

We consider a parabolic transmission problem, involving nonlinear fractional operators of different order, across a fractal interface $ \Sigma $. The transmission condition is of Robin type and it involves the jump of the $ p $-fractional normal derivatives on the irregular interface. After proving existence and uniqueness results for the weak solution of the problem at hand, via a semigroup approach, we investigate the regularity of the nonlinear fractional semigroup.

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Mathematics Subject Classification: Primary: 35R11, 47H20; Secondary: 28A80, 35B65, 47J35.

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Figure 1. The domain $ \Omega $

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