16 1.Linear Elliptic Equations We now require>0 and "<0.Hence, e≤w+(42+ where We write this as Lw≤λ("+aw+b)-1, where R We need to find a function in [0,D)such that w"+a+b=0in(0,D), "<0,'>0in(0,D),and(o)=0. First,general solutions of the ordinary differential equation above are given by 表尺叭是匠 (④=-8d+C-gea4 a 帝？ for some constants Ci and C2.For (0)=0,we need C1=C2/a.Hence we have,for some constant C. =-a+-e, a which implies v@=cew-&=e(c-&） "(d)=-Cae-ad. In order to have i D),we need C Then,i (0,D),and hence()=0 in (0,D).Therefore,we take 网=-2+总0ce01-6叫 平祖式美光然风花 -8a-6- Such a satisfies all the requirements we imposed. Now we estimate the modulus of continuity of solutions with the help of barrier functions constructed in Lemma 1.1.11. 由扫描全能王扫描创建由 扫描全能王 扫描创建