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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 15 - 24 (10page)
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Let N ≥ 1 and p > 1. Let
Ω be a domain of Rⁿ. In this article
we shall establish Kato’s inequalities for quasilinear degenerate elliptic operators of
the form Apu = divA(x,▽u) for u ∈ Kp(Ω
), where Kp(Ω
) is an admissible class and
A(x, €) :
×Rⁿ → Rⁿ is a mapping satisfying some structural conditions. If p = 2 for example,
then we have K₂(Ω
) = {u ∈ L¹
loc(Ω
) : αju, α²2
j,ku ∈ L¹
loc(Ω
) for j, k = 1, 2, · · · ,N}.
Then we shall prove that Ap|u| ≥ (sgn+ u)^p-1 and Apu+ ≥ (sgn+ u)^p−1Apu in D'(Ω
) with
u ∈ Kp(Ω
). These inequalities are called Kato’s inequalities provided that p = 2. The
class of operators Ap contains the so-called p−harmonic operators Lp = div(|▽u|^p−2▽u)
for A(x, €) = |€|^p−2€.
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참고문헌 (3)
참고문헌 신청
J. Garcia-Cuerva / 1985 / Rubio de Francia, Weighted norm inequalities and related Topics / North-Holland Mthematics Studies 116
T. Horiuchi / 2001 / Some remarks on Kato's inequality / J. of Inequalities and applications 6 : 29 ~ 36
T. Kato / 1972 / Schr¨odinger operators with singular potentials / Israel J. Math 13 : 135 ~ 148
T. Horiuchi / 2001 / Some remarks on Kato's inequality / J. of Inequalities and applications 6 : 29 ~ 36
T. Kato / 1972 / Schr¨odinger operators with singular potentials / Israel J. Math 13 : 135 ~ 148
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