Determination of a real parameter in the coefficient of a quasilinear elliptic differential equation (Q1188341)

Summary: We study the quasilinear elliptic differential equation \(\text{div}((b(u- u_ 0)^ l+c)\text{grad} u)=0\) with boundary value conditions of Dirichlet type in an \(n\)-dimensional cylinder. Provided we know the numbers \(u_ 0\), \(l\) and \(c\), the solution \(u\) on a plane which is parallel to the basic area of the cylinder, an eigenvalue and an eigenfunction of a certain eigenvalue problem, we give an explicit formula for the calculation of the real parameter \(b\).