Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A CHARACTERIZATION OF SOBOLEV SPACES BY SOLUTIONS OF HEAT EQUATION AND A STABILITY PROBLEM FOR A FUNCTIONAL EQUATION

  • Chung, Yun-Sung (BK21 MATH MODELING HRD DIV. DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY) ;
  • Lee, Young-Su (DEPARTMENT OF MATHEMATICSL SCIENCES KOREA ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY) ;
  • Kwon, Deok-Yong (DEPARTMENT OF MATHEMATICS SOGANG UNIVERSITY) ;
  • Chung, Soon-Yeong (DEPARTMENT OF MATHEMATICS AND PROGRAM OF INTEGRATED BIOTECHNOLOGY SOGANG UNIVERSITY)
  • Published : 2008.07.31
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Abstract

In this paper, we characterize Sobolev spaces $H^s(\mathbb{R}^n),\;s{\in}\mathbb{R}$ 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.

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References

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