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2000 | 75 | 3 | 281-287
Tytuł artykułu

The representation of smooth functions in terms of the fundamental solution of a linear parabolic equation

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
75
Numer
3
Strony
281-287
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-06-28
Twórcy
  • Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
Bibliografia
  • [1] D. G. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 22 (1968), 607-694.
  • [2] J. Chabrowski and N. A. Watson, Properties of solutions of weakly coupled parabolic systems, J. London Math. Soc. 23 (1981), 475-495.
  • [3] J. L. Doob, Classical Potential Theory and its Probabilistic Counterpart, Grund- lehren Math. Wiss. 262, Springer, 1984.
  • [4] A. M. Il'in, A. S. Kalashnikov and O. A. Oleĭnik, Linear equations of the second order of parabolic type, Uspekhi Mat. Nauk 17 (1962), no. 3, 3-146 (in Russian); English transl.: Russian Math. Surveys 17 (1962), no. 3, 1-143.
  • [5] E. P. Smyrnélis, Sur les moyennes des fonctions paraboliques, Bull. Sci. Math. 93 (1969), 163-173.
  • [6] N. A. Watson, Uniqueness and representation theorems for parabolic equations, J. London Math. Soc. 8 (1974), 311-321.
  • [7] N. A. Watson, Boundary measures of solutions of partial differential equations, Mathematika 29 (1982), 67-82.
  • [8] N. A. Watson, A decomposition theorem for solutions of parabolic equations, Ann. Acad. Sci. Fenn. Math. 25 (2000), 151-160.
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Bibliografia
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bwmeta1.element.bwnjournal-article-apmv75z3p281bwm
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