 Solution

ID: past-exam-of-the-methods-of-applied-functional-analysis-course-of-the-university-of-oxford/2010/a/3/b/i/solution

H_{0}^{1} (Ω)

and satisfies

\int_{Ω} \nabla u \cdot \nabla φ d x + \int_{Ω} (b \cdot \nabla u) φ d x = \int_{Ω} f φ d x (φ \in H_{0}^{1} (Ω)) .

b

and the Cauchy-Schwarz inequality make the drift term integrable. This weak formulation moves one derivative from the Laplacian onto the test function, while retaining the first-order drift term.

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