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A characterization of Sobolev spaces by solutions of heat equation and a stability problem for a functional equation

이영수|정순영|정윤성|권덕용
대한수학회 (The Korean Mathematical Society)|2008.07|대한수학회논문집 (Communications of the KMS)|제23권 제3호|pp. 401-411

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참고문헌

키워드

heat kernelCauchy functional equationSobolev space
주제분류수학

초록

In this paper, we characterize Sobolev spaces Hs(Rn), s ∈ R by the initial value of solutions of heat equation with a growth condition. By using an idea in its proof, we also discuss a stability problem for Cauchy functional equation in the Sobolev spaces.

Abstract

In this paper, we characterize Sobolev spaces Hs(Rn), s ∈ R by the initial value of solutions of heat equation with a growth condition. By using an idea in its proof, we also discuss a stability problem for Cauchy functional equation in the Sobolev spaces.

참고문헌 (11)

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  2. J. Chung, "Stability of functional equations in the space of distributions and hyperfunctions", J. Math. Anal. Appl, 286, pp.177~186 (2003)
  3. J. Chung, "The stability of Cauchy equations in the space of Schwartz distributions", J. Math. Anal. Appl, 295, pp.107~114 (2004)
  4. S.-Y. Chung, "A regularity theorem for the initial traces of the solutions of the heat equation", J. Korean Math. Soc, 33(4), pp.1039~1046 (1996)
  5. S.-Y. Chung, "Reformulation of some functional equations in the space of Gevrey distributions and regularity of solutions", Aequationes Math, 59, pp.108~123 (2000)
  6. S.-Y. Chung, "Bochner-Schwartz theorem for ultradistributions", J. Math. Anal. Appl, 228, pp.166~180 (1998)
  7. Y.-S. Chung, "Stability of a quadratic functional equation in the space of distributions", Math. Inequal. Appl, 9(2), pp.325~334 (2006)
  8. L. C. Evans, "Partial Differential Equations, G.S.M. Vol. 19" (1983), Americam Mathematical Society
  9. L. H¨ormander, "The Analysis of Linear Partial Differential Operators, Vol.1" (1983), Springer-Verlag
  10. Y.-S. Lee, "Stability of a quadratic Jensen type functional equation in the spaces of generalized functions", J. Math. Anal. Appl, 324, pp.1395~1406 (2006)
  11. T. Matsuzawa, "A calculus approach to hyperfunctions I", Nagoya Math. J, 108, pp.53~66 (1987)

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