- Tytuł:
- The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation
- Autorzy:
- Watson, Neil
- Tematy:
-
fundamental solution
parabolic equation
representation theorem - Pokaż więcej
- Data publikacji:
- 2000
- Powiązania:
- https://bibliotekanauki.pl/articles/1207895.pdf Link otwiera się w nowym oknie
- Źródło:
-
Annales Polonici Mathematici; 2000, 75, 3; 281-287
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Opis:
- Let L be a second order, linear, parabolic partial differential operator, with bounded Hölder continuous coefficients, defined on the closure of the strip $X = ℝ^{n} × ]0,a[$. We prove a representation theorem for an arbitrary $C^{2,1}$ function, in terms of the fundamental solution of the equation Lu=0. Such a theorem was proved in an earlier paper for a parabolic operator in divergence form with $C^{∞}$ coefficients, but here much weaker conditions suffice. Some consequences of the representation theorem, for the solutions of Lu=0, are also presented.
- Dostawca treści:
- Biblioteka Nauki
Artykuł