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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 4, 1991, pp. 439–446
DOI: 10.4171/ZAA/466

Published online: 1991-12-31

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

Sybille Handrock-Meyer[1]

(1) Technische Universität Chemnitz, Germany

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 $b$.

Keywords: Inverse problems, boundary value problems, quasilinear elliptic differential equations

Handrock-Meyer Sybille: Determination of a Real Parameter in the Coefficient of a Quasilinear Elliptic Differential Equation. Z. Anal. Anwend. 10 (1991), 439-446. doi: 10.4171/ZAA/466