Let {vα} be a system of polynomial solutions of the parabolic equation ahk∂xhxku-∂tu=0 in a bounded C1-cylinder ΩT contained in Rn+1. Here, ahk∂xhxk is an elliptic operator with real constant coefficients. We prove that {vα} is complete in Lp(Σ′), where Σ′ is the parabolic boundary of ΩT. Similar results are proved for the adjoint equation ahk∂xhxku+∂tu=0.
Completeness Theorems on the Boundary for a Parabolic Equation
Cialdea, A.
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2026-01-01
Abstract
Let {vα} be a system of polynomial solutions of the parabolic equation ahk∂xhxku-∂tu=0 in a bounded C1-cylinder ΩT contained in Rn+1. Here, ahk∂xhxk is an elliptic operator with real constant coefficients. We prove that {vα} is complete in Lp(Σ′), where Σ′ is the parabolic boundary of ΩT. Similar results are proved for the adjoint equation ahk∂xhxku+∂tu=0.File in questo prodotto:
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