W~lL_p(Φ)空间的迹定理与强非线性变分问题

我们在[1]中建立了 W~2Lp(Φ;E_n~ )的迹定理,但在[1]中是利用调和函数作反嵌入定理的,这个方法不适用于ι为任意的情形。在本文中我们将对任意的ι用平均函数作反嵌入定理,其思想来源于[2].然后把它应用于一般区域的、被积函数是指数型增长的多重积分的极小问题。     

ON THE INTERIOR REGULARITIES OF THE SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

In[1]we discussed the problems of calculus of variations withstrong nonlinearity.Its Euler equation is evidently the followingelliptic type equation of divergent form with strongly increasingcoefficients,(da(x,u,u_x))/(dx_) a(x,u,u_x)=0,x∈ΩR~n.(1)We get the interior regularities of the solutions of(1).It is justthe Hilbert's 19th problem in the ease with strong nonlinearity.     

大气湿度、燃油成份和燃气离解对发动机性能的影响及其在发动机性能计算通用程序中的应用

一、引言 在英国克朗菲尔德工学院热动力教研室代理主任的合作下,成功地建立了一个数学计算模型来考虑大气湿度、燃油成分和燃气离解对发动机性能的影响.并将程序化的模型应用到发动机性能计算通用程序中,建立了一个能模拟上述影响的通用程序‘TURB_FLEXI’.     

ON THE INTERIOR REGULARITIES OF THE SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

In we discussed the problems of calculus of variations with strong nonlinearity. Its Euler equation is evidently the following elliptic type equation of divergent form with strongly increasing coefficients,We get the interior regularities of the solutions of(1). It is just the Hilbert's 19th problem in the case with strong nonlinearity.