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answerhappygod
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- Problem 6 30 Let N 3 Denote Br Sh 1 Wn 1 Defined As In Problem 3 Suppose Fe C R F X 0 V1 1 1 1 1 (7.79 KiB) Viewed 17 times
hint： use Green‘s identity
Problem 6 [30]. Let n > 3, denote Br, Sh-1, wn(1) defined as in Problem 3. Suppose fe C (R"), f(x) = 0, V1|1|| > 1.
1. Prove that, Vp € R", lim - 0 los f(p – ) -1 wn (1)||2|| dS = (n - 2)f(p). 2. Let W, = R" Br, prove that p ER", -1 lim >0 Sw.wa(1)|| Afp- ) DV = (n - 2)f(p). n2 3. Set u(y) 1 = n- - 2 dan w.(1)– 2117-35 ()AV, VYER" -1 y afVy . Define Δ = a2 ay? 22 aya Prove that Au(y) = f(y), Vy € R".
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