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Characterization of sets of determination for parabolic functions on a slab by coparabolic (minimal) thinness. (English) Zbl 0887.35064
A set \(M \subset \mathbb R^n \times ]0,T[\) is said to be a set of determination, if \[ \inf u (\mathbb R^n\times ]0,T[)= \inf u (M) \] for every positive solution of the heat equation. In the paper (which complements the earlier article of the author [ibid. 35, 497-513 (1994; Zbl 0808.35043)], sets of determination are characterized in terms of parabolic limit points of \(M\) as well as of (minimal) coparabolic thinness of various “thickenings” of \(M\).
Reviewer: I.Netuka (Praha)
MSC:
35K05 Heat equation
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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