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Zeitschrift für Analysis und ihre Anwendungen

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Volume 11, Issue 3, 1992, pp. 401–406
DOI: 10.4171/ZAA/596

Published online: 1992-09-30

A Counterexample for $L^1$-Estimates for Parabolic Differential Equations

Pawel Kröger[1]

(1) Universidad Técnica Federico Santa María, Valparaíso, Chile

We show that the Dini (1) continuity of the coefficients of a linear parabolic differential operator in non-divergence form is in some sense the weakest condition such that the solutions of the corresponding initial value problem satisfy an $L^1$-estimate;…

Keywords: Initial value problems for second-order, parabolic equations, a priori estimates, diffusion processes

Kröger Pawel: A Counterexample for $L^1$-Estimates for Parabolic Differential Equations. Z. Anal. Anwend. 11 (1992), 401-406. doi: 10.4171/ZAA/596