Consider: V2u = f(x); x ∈ R" (bounded), B1u + B2∇u · n = g(x); x ∈ ∂Ω, with B1, B2 ∈ ℅

Consider: V2u = f(x); x ∈ R quot; (bounded), B1u + B2∇u · n = g(x); x ∈ ∂Ω, with B1, B2 ∈ ℠. Let ε ∈ ℠⠿ be arbitrary but fixed. Let G(x; ε) be the solution to (1) with f(x) = S(x; ε) and g(x) = 0, where S(x; ε) is the Dirac delta function. Show that G is symmetric in its arguments, i.e., G(x; ε) = G(ε; x). Assume B1 ≠0, B2 ≠0 [6 marks]: b) Show that for G(x, ε), we have ∇²G(u,v) = ∇²G(v, u), where u,v ∈ Ω [4 marks] (Hint: use the limit definition of partial derivatives).

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Видео Consider: V2u = f(x); x ∈ R" (bounded), B1u + B2∇u · n = g(x); x ∈ ∂Ω, with B1, B2 ∈ â„… канала Ellie Clark