Study of a singular equation set in the half-space
Résumé
This work is dedicated to the resolution of a singular equation set in the half-space, with a diffusion coe cient that blows up on the boundary. More precisely, for a datum g : R3 → R, our problem consists in seeking u : R3 → R formally solution to: −div(1/x3 grad u) = g in R3, u = 0 on Γ = R2 × {0} . We give existence and uniqueness results of weak and strong solutions in suitable weighted spaces, where the weight depends on x3 .
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