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一个退缩椭圆方程的反问题
An Inverse Problem for a Degenerate Elliptic Equation
【摘要】 考虑了退缩椭圆方程的反问题(1.1)~(1.4),在一定条件下证明了广义解的存在性和唯一性。
【Abstract】 in this paper we study the inverse problem of the form and prove the following theorem:Theorem 1 Suppose that the following conditions are satisfied:whereThen the problem (1.1)~(1.4) at least has one solution (p(x), v(x,y)) with p(x)∈C~0([0,1]), and v(x,y), v_y(x,y)∈C~0([0,1]×[0,1]), v_x~’(X,y)∈L~s([0,1]×(0,1]), Ifρ<1/2, then the problem(1.1)~(1.4) cannot have more than one solution.
【关键词】 反问题;
退缩椭圆方程;
广义解;
存在性;
唯一性;
【Key words】 Inverse problem; degenerate elliptic equation; generalized solu tion; existence; uniqueness.;
【Key words】 Inverse problem; degenerate elliptic equation; generalized solu tion; existence; uniqueness.;
- 【文献出处】 吉林大学自然科学学报 ,Journal of Jilin University , 编辑部邮箱 ,1988年02期
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