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Zeitschrift für Analysis und ihre Anwendungen


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Volume 3, Issue 5, 1984, pp. 457–479
DOI: 10.4171/ZAA/122

Published online: 1984-10-31

Einige Bemerkungen zur Anfangs-Randwertaufgabe $\frac{\partial}{\partial t} u - h(x, t) \Delta u =f$ mit meßbarem Koeffizienten

Jörg Heinrich

In the present paper the mixed problem $\frac{\partial}{\partial t} u - h(x, t) \Delta u =f$ with measurable coefficient is considered at first for special domains (cubes) by a modification of Banach’s fixed point theorem. Starting from this we get an existence and uniqueness theorem for domains of the class $O^2$. Several properties of the solution are discussed.

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Heinrich Jörg: Einige Bemerkungen zur Anfangs-Randwertaufgabe $\frac{\partial}{\partial t} u - h(x, t) \Delta u =f$ mit meßbarem Koeffizienten. Z. Anal. Anwend. 3 (1984), 457-479. doi: 10.4171/ZAA/122