CHEGARALANGAN UCH O‘LCHOVLI SOHADA ELLIPTIK TIPLI TENGLAMALAR SISTEMASI UCHUN KOSHI MASALASI MUNDARIJA KIRISH ……….........................................................................................................3 I BOB. ELLIPTIK TIPLI TENGLAMALAR VA ULARNING YECHIMLARI XOSSALLARI 1.1-§ Elliptik tipli tenglamalar uchun asosiy chegaraviy masalalar………………13 1.2-§ Laplas tenglamasining fundamental yechimlari………..…………………… 18 1.3-§ Garmonik funksiyalar va ularning xossalari………………………………… 21 1.4-§ Gel’mgol’s tenglamasi uchun integral formula. Grin funksiyasi …………..27 Xulosa……………………………………………………………………………..34 II BOB. BIRINCHI TARTIBLI ELLIPTIK TIPLI TENGLAMALAR SISTEMA UCHUN INTEGRAL FORMULA 2.1-§ Matritsalar sinfi ………………………………...……………………...…...35 2.2-§ Birinchi tartibli elliptik tipli tenglamalar sistema uchun integral formula….38 2.3-§ Birinchi tartibli elliptik tipli tenglamalar sistema uchun misollar………… . 40 2.4-§ Birinchi tartibli elliptik tipli tenglamalar sistema uchun Morera teoremasi……………………………………………………….…..…… .. 46 Xulosa…………………………………………………………………….……….48 III BOB. BIRINCHI TARTIBLI ELLIPTIK TIPDAGI TENGLAMALAR SISTEMASI UCHUN KOSHI MASALASI 3.1-§ Koshi masalasining qo‘yilishi………………..…………………………….49 3.2-§ Maxsus sohada elliptik tipli sistemaga qo‘yilgan Koshi masalasini yechishda Karleman matritsasi……………………………….………………………………54 3.3-§ Birinchi tartibli elliptik tipli sistema uchun qo‘yilgan Koshi masalasini regulirizatsiyasi……………………………………..……………………………..56 XULOSA …………………………………………………………………………67 FOYDALANILGAN ADABIYOTLAR ………………………………………. . 69