On a regularity theorem in rectangular domains
Mitsuharu Ôtani, Tetsuya Koyama, Yusuke Yamauchi · LIBERTAS MATHEMATICA (new series) · 2016
The aim of this note is to prove a regularity theorem for an elliptic boundary value problem on a rectangular domain Ω. We prove that weak solution of u-Δu=G with boundary value f∈H²(∂Ω) belongs to H²(Ω).