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Rectifiable oscillations of radially symmetric solutions of p-Laplace differential equations

We study a kind of geometric oscillatory and asymptotic behaviour near |x| = 1 of all radially symmetric solutions u = u(x) of the p-Laplace partial differential equation (P). Necessary and sufficient conditions on the coefficient f (|x|) are given such that u(x) oscillates near |x| = 1 and the surface area of graph Γ(u) ⊆ RN+1 of u(x) is finite-rectifiable oscillations, and infinite-nonrectifiable oscillations. The L1 - integrability and Lp -nonintegrability of |∇u| on Ω for p > 1 are also considered.

p-Laplacian equation; radially symmetric solutions; oscillations; surface area; rectifiability

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