Finsler Hardy–Kato's inequality

Abstract

We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtained by [3] in Euclidean context. Also we discuss the validity of the same type of inequalities on open cones.

Asymptotic behavior of least energy solutions to the Finsler Lane-Emden problem with large exponents

“…If we assume that Hess(H q (ξ)) is positive definite on R N \ {0}, Q q becomes a uniformly elliptic operator locally. The Finsler q-Laplacian has been widely investigated in literature by many authors in different settings, see [2], [5], [8], [9], [10], [12], [13], [14], [17], [20] [34] and the references therein.…”

Finsler Hardy inequalities

“…The Finsler Laplacian has been widely investigated in literature and its notion goes back to the work of G. Wulff, who considered it to describe the theory of crystals. Many other authors developed the related theory in several settings, considering both analytic and geometric points of view, see ([4], [2], [12], [13], [14], [18], [20], [21] and references therein).…”

“…Remark 6.7. Let Ω ⊂ ℝ + be a domain with a flat boundary portion on ℝ + , that is, 4 ⊂ Ω for some > 0where4 be an open cube as in (6.12). Then we have (Ω) =…”

Applications of $p$-harmonic transplantation for functional inequalities involving a Finsler norm

“…The resulting inequalities include a general norm (Finsler norm) with the precise information on the extremizers of the best constant involved. For other inequalities involving Finsler norms, we refer to [1], [16], [26], [29], [36], [37], [39], and the references therein..…”