zbMATH — the first resource for mathematics

Remarks on the global Sobolev inequalities in the Minkowski space \({\mathbb{R}}^{n+1}\). (English) Zbl 0686.46019
The inequalities referred to in the title were first introduced by the author [same journal 38, No.3, 321-332 (1985; Zbl 0635.35059)] and developed further by L. Hörmander [“On Sobolev spaces associated with some Lie algebras”, Current topics in partial differential equations. Pap. dedic. Shizohata Occas. 60th birthday, 261-287 (1986; Zbl 0658.46023)] and the author [Nonlinear systems of partial differential equations in applied mathematics, Part 1 (Santa Fe, N.M., 1984), 293-326, Am. Math. Soc., Providence, R.I. (1986; Zbl 0599.35105)]. The present paper contains a simpler derivation of the inequalities based on the classical Sobolev inequality and a scaling argument.

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35L70 Second-order nonlinear hyperbolic equations
58D15 Manifolds of mappings
Full Text: DOI
[1] Klainerman, Comm. Pure Appl. Math. 38 pp 321– (1985)
[2] On Sobolev spaces associated with some Lie algebras, Report 4, 1985, Inst. Mittag-Leffler.
[3] Klainerman, Lectures in Appl. Math. 23 pp 293– (1986)
[4] Klainerman, Comm. Pure Appl. Math. 38 pp 631– (1985)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.