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

Simone Creo | Zendy; Maria Rosaria Lancia | Zendy; Paola Vernole | Zendy

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Transmission 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 - 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.

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