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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.
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참고문헌 (11)
참고문헌 신청
J. A. Baker / 2001 / Distributional methods for functional equations / Aequationes Math 62 : 136 ~ 142
J. Chung / 2003 / Stability of functional equations in the space of distributions and hyperfunctions / J. Math. Anal. Appl 286 : 177 ~ 186
J. Chung / 2004 / The stability of Cauchy equations in the space of Schwartz distributions / J. Math. Anal. Appl 295 : 107 ~ 114
L. C. Evans / 1983 / Partial Differential Equations, G.S.M. Vol. 19 / Americam Mathematical Society
L. H¨ormander / 1983 / The Analysis of Linear Partial Differential Operators, Vol.1 / Springer-Verlag
J. Chung / 2003 / Stability of functional equations in the space of distributions and hyperfunctions / J. Math. Anal. Appl 286 : 177 ~ 186
J. Chung / 2004 / The stability of Cauchy equations in the space of Schwartz distributions / J. Math. Anal. Appl 295 : 107 ~ 114
L. C. Evans / 1983 / Partial Differential Equations, G.S.M. Vol. 19 / Americam Mathematical Society
L. H¨ormander / 1983 / The Analysis of Linear Partial Differential Operators, Vol.1 / Springer-Verlag
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