Mohammad El Smaily

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math.AP2024

The principal eigenvalue of a mixed local and nonlocal operator with drift

Craig Cowan, Mohammad El Smaily, Pierre Aime Feulefack

We study the eigenvalue problem involving the mixed local-nonlocal operator $L := - I^ + (- I^)^{s} + q \cdot \nabla$ ~ in a bounded domain $I^c ◯ \subset R^{N},$ where a Dirichlet condition is p…

math.AP2024

Existence and regularity results for a Neumann problem with mixed local and nonlocal diffusion

Craig Cowan, Mohammad El Smaily, Pierre Aime Feulefack

In this paper, we consider an elliptic problem driven by a mixed local-nonlocal operator with drift and subject to nonlocal Neumann condition. We prove the existence and uniqueness…