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math.AP2022
Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension
Thomas Alazard, Martina Magliocca, Nicolas Meunier
We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate…
math.AP2022★ 1 cited
Refined Rellich boundary inequalities for the derivatives of a harmonic function
Siddhant Agrawal, Thomas Alazard
The classical Rellich inequalities imply that the -norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined…