力学中泛函分析和变分原理第十讲.pdfVIP

鐮旂┒鐢熻绋 鍔涘涓殑娉涘嚱鍒嗘瀽 涓庡彉鍒嗗師鐞 绗崄璁诧細鏈夌晫绾挎€ф硾鍑戒笌鍏辫江绌洪棿 鎺堣鏁欏笀锛氶儹鏃暀鎺 澶ц繛鐞嗗伐澶у宸ョ▼鍔涘绯 璇 绋 鍥 椤 鍏辫江绠楀瓙 飦 璁卷祻鍜岉祼 涓虹嚎鎬ц祴鑼冪┖闂达紝饊偗 鈭 饊厓 淼? 淼 ,缁欏畾肀 鈭 鈭 淼愨垪 (淼愨垪 涓哄畾涔夊湪淼 涓婄殑鎵€鏈 鏈夌晫绾挎€ф硾鍑界殑绌洪棿饊厓 淼? 鈩 ,鍗稠祼 鐨勫叡杞┖闂?,鍒欐湁琛ㄨ揪寮忥細饊偗 肀 , 肀 鈭 , 鈭€肀 鈭 淼? 饊偗 肀 = 肀 鈭 淼 ,鏄祻涓婄殑娉涘嚱锛屽嵆 饊寫 肀 = 饊偗 肀 , 肀 鈭 = 肀? 饊偗 鈭 肀 鈭 鈭 鈭 鈭 鈭 鈭 鈭 飦 绠楀瓙饊偗 鏄畾涔夊湪淼 涓婄殑锛屼笖饊偗 鈭 饊厓 淼 , 淼 .绠楀瓙饊偗 绉颁负饊偗 鐨勫叡杞畻瀛愩€ Hilbert绌洪棿涓殑鍏辫江绠楀瓙 飦 鐢变簬鈩嶁垪 = 鈩?鏁呭浜庣敱鈩嶅埌鈩嶇殑鏈夌晫绾挎€х畻瀛愷€倻 ,鍏跺叡杞畻瀛愷€倻鈭 鐢变笅寮忕‘瀹氾細 饊倻 肀 , 肀 = 肀? 饊倻鈭 肀 濡傛灉饊倻 = 饊倻鈭 ,鍒欑О饊倻 鏄嚜鍏辫江绠楀瓙銆 姝ｄ氦(鍏冪礌涓庣畻瀛?銆佹浜よˉ 飦 鑻 肀? 鈩 = 0,鍒欑О鍏冪礌肀 鈭 淼 涓庘劚 鈭 淼忊垪 鏄浜ょ殑銆 飦 璁攫€厞鏄祻 鐨勫瓙闆嗭紝鍒欎笌饊厞涓瘡涓€涓厓绱犲潎姝ｄ氦鐨勬湁鐣岀嚎鎬ф硾鍑界殑鍏ㄤ綋锛岃涓吼€厞鈯 , 绉颁负饊厞鐨勬浜よˉ锛屾湁 鈯 鈭 饊厞 = 鈩 鈭 淼 ; 肀? 鈩 = 0, 肀 鈭 饊厞 璇 绋 鍥 椤 涓€闃跺彉鍒 飦 璁卷祻涓虹嚎鎬ц祴鑼冪┖闂达紝饊倷0 鈭 淼 . 鈩 饊倷 鏄湪饊倷0鍙婂叾閭诲煙鍐呮湁瀹氫箟鐨勬硾鍑斤紝瀵逛换 鎰忦€倝 鈭 淼 ,鑻ユ瀬闄恖im 鈩 饊倷0 +饊仭饊倝 鈭掆劚 饊倷0 瀛樺湪锛岃涓吼€嬁鈩 饊倷0; 饊倝 , 鍒欑О涓烘硾鍑解劚 鍦€倷0澶 饊仭鈫? 饊仭 鍏充簬澧為噺饊倝 鐨勪竴闃跺彉鍒嗐€傝嫢浠ゐ€寫 肀 = 鈩 饊倷0 + 肀○€倝 ,涓烘櫘閫氱殑涓€鍏冨嚱鏁帮紝鏄剧劧 饊寫鈥 0 = lim 饊寫 饊仭 鈭掟€寫 0 = 饊嬁鈩 饊倷0; 饊倝 ,涔熷彲鍐欎綔 饊仭鈫? 饊仭 饊嬁鈩 饊倷0; 饊倝 = 饊亼 鈩 饊倷0 + 肀○€倝 5.1.1 饊亼肀 饊仭=0 飦 鑻?5.1.1)涓€嬁鈩 饊倷0; 饊倝 鏄叧浜庰€倝鐨勬湁鐣岀嚎鎬ф硾鍑斤紝璁颁负鈩 鈥 饊倷0 ,鏈夛細饊嬁鈩 饊倷0; 饊倝 = 饊倝, 鈩 鈥 饊倷0 , 鍒欑О娉涘嚱鈩卞湪饊倷0澶勬槸鍔犳墭鍙井鐨勩€ 飦 琛ㄨ揪寮忦€亼鈩 饊倷0; 饊倝 = 饊倝, 鈩 鈥 饊倷0 = 鈩 鈥 饊倷0 饊倝, 绉颁负娉涘嚱鈩卞湪饊倷0澶勫叧浜庡閲忦€倝鐨勫姞 鎵樺井鍒嗐€ 飦 鏈夌晫绾挎€ф硾鍑解劚 鈥 饊倷0 绉颁负娉涘嚱鈩卞湪饊倷0澶勭殑鍔犳墭瀵兼暟銆 璇 绋 鍥 椤 涓€闃跺彉鍒嗙畻渚 飦 璁卷饱