Kato's inequality

In functional analysis, a subfield of mathematics, Kato's inequality is a distributional inequality for the Laplace operator or certain elliptic operators. It was proven in 1972 by the Japanese mathematician Tosio Kato.[1]

The original inequality is for some degenerate elliptic operators.[2] This article treats the special (but important) case for the Laplace operator.[3]

  1. ^ Kato, Tosio (1972). "Schrödinger operators with singular potentials". Israel Journal of Mathematics. 13 (1–2): 135–148. doi:10.1007/BF02760233. S2CID 115546931.
  2. ^ Devinatz, Allen (1979). "On an Inequality of Tosio Kato for Degenerate-Elliptic Operators". Journal of Functional Analysis. 32 (3): 312–335. doi:10.1016/0022-1236(79)90043-0.
  3. ^ Brezis, Haı̈m; Ponce, Augusto (2004). "Kato's inequality when Δu is a measure". Comptes Rendus Mathematique. 338 (8): 599–604. doi:10.1016/j.crma.2003.12.032.