Determination of a Real Parameter in the Coefficient of a Quasilinear Elliptic Differential Equation

Abstract

We study the quasilinear elliptic differential equation $\mathrm{div}((b(u–u_o{)}^1+c)\mathrm{grad}u)=0$ with boundary value conditions of Dirichlet type in an $n$-dimensional cylinder. Provided we know the numbers $u_o$, $I$ 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 $b$.