An existence and uniqueness theorem for the solution of an inverse problem for an elliptic equation
Considered is the inverse problem of determining the right hand side \( f(x)+g(y)\) of the following elliptic equation NEWLINE\[NEWLINE a(x,y)u_{xx}(x,y) + b(x,y)u_{yy}(x,y)= f(x)+g(y), NEWLINE\]NEWLINE where \(0<x<x_0\), \(0<y<y_0\). The conditions \( u_x(0,y)= u_x(x_0,y)= u_y(x,0)= u_y(x,y_0)=0, u(0,y)=\beta(y), u(x,0)=\delta(x)\) and functions \( a(x,y)>0, b(x,y)>0, \beta(y), \delta(x)\) are given. The author proves a theorem on local existence and uniqueness of solution to the inverse problem.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00006].
scientific article; zbMATH DE number 1602258