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

Pawel Kröger

doi:10.4171/zaa/596

JournalszaaVol. 11, No. 3pp. 401–406

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

Pawel Kröger
Universidad Técnica Federico Santa María, Valparaíso, Chile

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Abstract

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;…

Cite this article

Pawel Kröger, A Counterexample for $L^{1}$ -Estimates for Parabolic Differential Equations. Z. Anal. Anwend. 11 (1992), no. 3, pp. 401–406

DOI 10.4171/ZAA/596