Open AccessTransmission problems for the fractional $ p $-Laplacian across fractal interfaces
Author(s) -
Simone Creo,
Maria Rosaria Lancia,
Paola Vernole
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022047
Subject(s) - semigroup , uniqueness , mathematics , fractal , fractional laplacian , transmission (telecommunications) , nonlinear system , jump , order (exchange) , fractional calculus , pure mathematics , mathematical analysis , computer science , physics , telecommunications , quantum mechanics , finance , economics
We consider a parabolic transmission problem, involving nonlinear fractional operators of different order, across a fractal interface \begin{document}$ \Sigma $\end{document} . The transmission condition is of Robin type and it involves the jump of the \begin{document}$ p $\end{document} -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.