Question
Download Solution PDFLet B(0,1) = {(x,y) ∈ ℝ2|x2 + y2 < 1} be the open unit disc in ℝ2, ∂B(0, 1) denote the boundary of B(0,1), and v denote unit outward normal to ∂B(0, 1). Let f : ℝ2 → ℝ be a given continuous function. The Euler-Lagrange equation of the minimization problem
\(\rm min \left\{\frac{1}{2}\iint_{B(0,1)}|\nabla u|^2dxdy+\frac{1}{2}\iint_{B(0, 1)}e^{u^2}dxdy+∈t_{\partial B(0, 1)}fuds\right\}\)
subject to u ∈ C1 \(\rm \overline{B(0, 1)}\) is
Answer (Detailed Solution Below)
Detailed Solution
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Last updated on Jun 5, 2025
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