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98 EHFHGHKHD H;H>GHCKFR:GGHCA:>:Q >EYMJ: −1\u ε 1 1 ihegy_lky g_jZ\_gkl\h | ∇u | ≤ c | x − x( d) | ]^_ x → x(d) b d = a n beb d = b n , n = 1, , N . 1 1 Γ : ∗ *>hdeZ^hlf_q_g`xjbdZdh^bgbaemqrbogZih^k_dpbb
Ih^k_dpbyfZl_fZlbdb 99 < hij_^_e_gbb deZkkZ K nmgdpbb u(x) b ∇u(x) g_ij_ju\gh ijh^he`bfu gZ 1 1 jZaj_au Γ \ X ke_\ZbkijZ\Zghfh]mlbf_lvkdZqhdijbi_j_oh^_q_j_a Γ \ X . AZ^ZqZU. GZclbnmgdpbx u(x) badeZkkZK, dhlhjZym^h\e_l\hjy_lmjZ\g_gbx =_evf]hevpZ b]jZgbqgufmkeh\byf 2 1 ∆u ( x) + k u( x) = 0, x ∈ D \ Γ , k = const, Im k > 0 ∂u( x) + & = F ( s) , ∂n + x ( 1) x( s) ∈Γ ∂u( x) − & = F ( s) , u( x) 2 = F( s) . (1) x ( s) ∈ Γ ∂n − x ( 1) x( s) ∈Γ keb D —\g_rgyyh[eZklv^h[Z\bfmkeh\bygZ[_kdhg_qghklb u(x) ]^_ − 2 ( | | 1/ − 2 u = o x ), | ( ) | ( | | 1/ 2 ∇ x = o x ) | = x1 + − 0, λ 1 1, 2 L_hj_fZkeb F ( s), F ( s) ∈ C ( Γ ), F( s) ∈C λ ( Γ ) 2 u , | x + x → ∞ . lhdeZkkbq_kdh_j_r_gb_ aZ^ZqbU kms_kl\m_lb_^bgkl\_gghHgh\ujZ`Z_lkynhjfmehc i u [ µ ]( x) = w [ ]( x) w [ ]( ) d , (2) + − (1) ∫[ F ( s) −F ( s) ] H ( k | x − y( σ ) | ) 0 1 µ + 2 µ σ + σ 4 1 Γ Γ ( k | x − y( σ ) | ) (1) i ∂H 0 i w1[ µ ]( x) = ∫µ ( σ ) & dσ , w 2[ µ ]( x) = 4 2 ∂n ∫ µ ( σ ) V ( x, σ ) dσ , 4 1 ( k | x− y( ξ) | ) σ (1) ∂H0 V ( x, σ) = ∫ & dξ , ∈ 1 [ a ] 1 n , b n y 1 ∂n σ , a y n (1) p 1 0 2 ]^_ H 0 ( z) — nmgdpby OZgd_ey i_j\h]h jh^Z [1], µ ( s) ∈C1/ 2( Γ ) C ( Γ ) ( p = min{ 1/ 2, λ} ) — j_r_gb_ kbkl_fu bgl_]jZevguo mjZ\g_gbc ihemqZxsboky ijb ih^klZgh\d_\bm^h\e_l\hjyxs__mkeh\byf LZdh_j_r_gb_kms_kl\m_lb_^bgkl\_ggh 1 n b ∫ µ ( σ ) dσ = 0 , n = 1, N1 . 1 n a 1. Gbdbnhjh\ :N M\Zjh\ D BAMQGB>JCN:DHGLJ:KLGUOKLJMDLMJ
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