Elliptic Problems and the Variational form
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Date
2024-09
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Addis Ababa University
Abstract
In this thesis, given a bounded domain Ω⊂𝑅𝑛. we focus on the variational form
∫ Ω{𝛼∇𝑢⋅∇𝜙+𝑎𝑢𝜙}𝑑𝑥=∫ Ω𝑓𝜙𝑑𝑥,𝜙∈𝐻01(Ω)
Of an elliptic problem,
−𝛼Δ𝑢+𝑎(𝑥)𝑢=𝑓,𝑖𝑛 Ω
With various conditions (Dirichlet, Neumann, and Robin) on boundary 𝜕Ω. We provide some general results on uniqueness and also find sub (supper)-solutions with in the frame work of variational setting.
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Keywords
Elliptic Problems, Variational form