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

  • Sybille Handrock-Meyer

    Technische Universität Chemnitz, Germany

Abstract

We study the quasilinear elliptic differential equation div((b(uuo)1+c)gradu)=0\mathrm {div}((b(u–u_o)^1 + c) \mathrm {grad}u) = 0 with boundary value conditions of Dirichlet type in an nn-dimensional cylinder. Provided we know the numbers uou_o, II and cc, 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 bb.

Cite this article

Sybille Handrock-Meyer, Determination of a Real Parameter in the Coefficient of a Quasilinear Elliptic Differential Equation. Z. Anal. Anwend. 10 (1991), no. 4, pp. 439–446

DOI 10.4171/ZAA/466