Naslov
Rectifiability of solutions of the one-dimensional p-Laplacian

Autori
Pašić, Mervan

Izvornik
Electronic journal of differential equations (1072-6691) 2005 (2005), 46; 1-8

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
nonlinear p-Laplacian ; bounded continuous solutions ; qualitative properties ; graph ; length ; rectifiability

Sažetak
In the recent papers [8] and [10] a class of Carathéodory functions ƒ(t, η, ξ) rapidly sign-changing near the boundary point t = α, has been constructed so that the equation -(|y'|p-2y')' = ƒ(t, y, y') in (α, b) admits continuous bounded solutions y whose graphs G(y) do not possess a finite length. In this paper, the same class of functions ƒ(t, η, ξ) will be given, but with slightly different input data compared to those from the previous papers, such that the graph G(y) of each solution y is a rectifiable curve in ℝ2. Moreover, there is a positive constant which does not depend on y so that length (G(y)) ≤ c < ∞.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA